- Difference: Syllogism vs Logical connectives
- Standard format: logical connectives
- Logical connective: if then
- Logical connective: Only IF
- Logical Connective: UNLESS
- Logical connective: otherwise
- Logical connective: When, Whenever, every time
- Logical Connective: Either OR
- Demo Q: Only if: bored TV brother (CSAT 2012)
- Demo Q (If, then) Professor Headaches (CAT’98)
- Demo Q: Either or: derailed/late train (CAT’97)
Difference: Syllogism vs Logical connectives
Syllogism (all cats are dog) is a common and routinely appearing topic in most of the aptitude exams (Bank PO, LIC, SSC etc). But Logical connectives is rare. However, in UPSC CSAT 2012 the topic was asked, therefore, you’ve to prepare it.
Syllogism |
Logical connectives |
| Contains words like “all, none, some” etc. Can be classified into UP, UN,PP and PN. Already explained in previous articles. | Contains words like “if, unless, only if, whenever” etc. can be classified into 1, ~1, 2, ~2 (we’ll see in this article) |
| Have to mugup more formulas, takes more time than logical connective questions. | Less formulas and quicker than syllogism. |
Question Statements:
Conclusion choices:
|
Question statements:
Conclusion choices:
|
Standard format: logical connectives
- If, unless, only if, whenever, every time etc. are examples of Logical connectives.
- Whenever you’re given a question statement, first rule is: question statement must be in the standard format.
- The standard format is
- ****some logical connective word *** simple statement#1, simple statement #2.
- It means, the question statement must start with a logical connective word, otherwise exchange position. For example
| Given question statement | Exchange position? |
| If you’re in the army, you’ve to wear uniform |
|
| You’ve to wear uniform, if you’re in the army |
|
| You’ve to salute, whenever Commanding Officer comes in your cabin. |
|
Now let’s derive valid inferences for various logical connectives.
Logical connective: if then
Consider these two simple statements
- You’re in army
- You’ve to wear uniform.
These are two simple statements. Now I’ll combine these two simple statements (#1 and #2) to form a complex statement.
- If you’re in army(#1), you have to wear uniform.(#2)
What about its reverse?
- You’ve wearing uniform (#2)—> that means you’re in the army.(#1)
- But there is possibility, you’re in navy—-> you’ll still have to wear a uniform. It means,
- if 1=>2, then 2=>1 is not always a valid inference.
- Let’s list all such scenarios in a table.
| Given statement:If you’re in army(#1), you have to wear uniform.(#2) | ||
| Inference? | Valid / invalid? | |
|
If you’ve to wear uniform, you’re in army. | you’ve to wear uniform in navy, air force, BSF etc. so this inference is not always valid. |
|
if you’re not in army, you don’t have to wear uniform. | you’ve to wear uniform in navy, air force, BSF etc. so this inference is not always valid. |
|
If you don’t have to wear uniform, you’re not in army. | Always valid. |
- In the exam, you don’t have to think ^that much. Just mugup the following rule:
- Given statement =“If #1 then #2”, in such situation the only valid inference is “if Not #2, then not #1”.
- In other words, “if 1st happens then 2nd happens”, in such situation, the only valid inference is “if 2nd did not happen then 1st did not happen”.
- Now I want to construct a short and sweet reference table for the logical connective problems. So I’ll use the symbol ~= negative.
~1=meaning NOT 1 ( or in other words, negative of #1)
| Given | Valid inference |
| If 1, then 2 | If not 2, then not 1 |
| If 1=>2 | ~2=>~1 |
- In some books, material, sites, you’ll find these rules explained as using “P” and “Q” instead of 1 and 2.
- But in our method, you first make sure the given (complex) statement starts with a logical connective (or you exchange position as explained earlier)
- We denote the first simple sentence as #1 and second simple sentence as #2.
- The reason for using 1 and 2= makes things less complicated and easier to mugup.
Logical connective: Only IF
- In such scenario, you’ve to rephrase given statement into “if then” and then apply the logical connective rule for “if then”.
- For example: given statement: he scores a century, only if the match is fixed.
- The “standard format”= only if the match is fixed(1), he scores a century(2).
- In case of “only if”, we further convert it into an “if” statement, by exchanging positions. That is
- if he scores a century(#2), the match is fixed(#1).
- Then apply the formula for “if then” and get valid inference.
- Here we’ve “if 2=>1” as per our formula for “if then”, the valid inference will be ~1=>~2. Don’t confuse between 1 and 2. Because essentially the valid inference is “negative of end part => negative of starting part”.
- Therefore “if 2=>1 then ~1=~2”
- similarly “if 98=>97, then valid inference will be ~97=>~98”
- Similarly “if p=>q, then valid inference will be ~q=>~p”,
- similarly “if b=>a, then valid inference will be ~a=~b”) .
- Update our table
| Logical connective | Given statement | Valid inference using symbol | Valid inf. In words |
| If | If 1=>2 | ~2=>~1 | Negative of end part=> negative of start part |
| Only if | Only if 1=>2 | ~1=>~2 | Negative of start part=>negative of end part. |
Logical Connective: UNLESS
- Given statement: Unless you bribe the minister(#1), you will not get the 2G license.(#2)
- Unless = if…..not.
- So, I can re-write the given statement as
- (new) Given statement: If you don’t bribe the minister(#1), you’ll not get the 2G license.(#2)
How to come up with a valid inference here?
| #1 | You don’t bribe the minister |
| #2 | You’ll not get the 2G license. |
- For “if..then”, We’ve mugged up the rule: 1=>2 then only valid inference is ~2=>~1. (in other words, negative of end part => negative of starting part).
- let’s construct the valid inference for this 2G minister.
- we want ~2 => ~1
- Negative of (2) => negative of (1)
- Negative of (you’ll not get the 2G license)=>negative of (you don’t bribe the minister)
- You’ll get the 2G license => you bribe the minister.
- In other words, If I see a 2G license in your hand, then I can infer that you had definitely bribed the minister.
- This is one way of doing “unless” questions = via converting it into “if…not” type of statement.
- The short cut is to mugup another formula: unless1=>2 then ~2=>1.
- How did we come up with above formula?
Deriving the formula for unless
- Unless 1=>2 (given statement)
- if not 1=>2 (because unless=if not)
- if ~1=>2 (I’m using symbol ~ instead of “not”)
- ~2=> ~(~1) (because we already mugged up the rule “if 1=>2, then valid inference is ~2=>~1)
- ~2=>1 (because ~(~1) means double negative and double negative is positive hence ~(~1)=1)
This is our second rule: Unless1=>2 then ~2=>1
Table
| Logical connective | Given statement | Valid inference using symbol | Valid inf. In words |
| If | If 1=>2 | ~2=>~1 | Negative of end part=> negative of start part |
| Only if | Only if 1=>2 | ~1=>~2 | Negative of start part=>negative of end part. |
| Unless | Unless 1=>2 | ~2=>1 | Negative of end part=>start part unchanged. |
Logical connective: otherwise
- Suppose given statement is: 1, otherwise 2.
- you can write it as unless 1 then 2. (unless1=>2)
- Then use the formula for “unless.”
Logical connective: When, Whenever, every time
- Given statement: he scores century, when match is fixed.
- This is not in standard format of “**logical connective word**, simple statement #1, simple statement #2.”
- So first I need to exchange the positions: “when match is fixed (#1), he scores century (#2)”.
- In case of when and whenever, the valid inference is= same like “If, then”. That means negative of end part=>negative of starting part.
- Same formula works for “whenever” and “Everytime”.
- Update the table
| Logical connective | Given statement | Valid inference using symbol | Valid inf. In words |
| If | If 1=>2 | ~2=~1 | Negative of end part=> negative of starting part |
| When | When 1=>2 | ||
| Whenever | Whenever 1=>2 | ||
| Everytime | Everytime 1=>2 | ||
| Only if | Only if 1=>2 | ~1=>~2 | Negative of start part=>negative of end part. |
| Unless | Unless 1=>2 | ~2=>1 | Negative of end part=>starting part unchanged. |
Logical Connective: Either OR
Given statement: Either he is drunk(1) or he is ill(2).
In such cases, if not 1 then 2. And if not 2 then 1.
Meaning,
- if he is not drunk then he is definitely ill
- if he is not ill, then he is definitely drunk
both are valid. Update the table
| Logical connective | Given statement | Valid inference using symbol | Valid inf. In words |
| If | If 1=>2 | ~2=~1 | Negative of end part=> negative of starting part |
| When | When 1=>2 | ||
| Whenever | Whenever 1=>2 | ||
| Everytime | Everytime 1=>2 | ||
| Only if | Only if 1=>2 | ~1=>~2 | Negative of start part=>negative of end part. |
| Unless | Unless 1=>2 | ~2=>1 | Negative of end part=>starting part unchanged. |
| Otherwise | 1 otherwise 2=> rewrite as Unless1=>2. | ||
| Either or | Either 1 or 2 |
|
Negative of any one part=> remaining part remains unchanged. |
- Now let’s solve some questions from old CSAT and CAT papers
- Please note: in the exam, actual wording / meaning of the simple statement doesn’t matter. Just apply the formulas as given in above table.
- For example, “if you’re in army, you have to wear uniform.” Then valid inference is ~2=>~1 (you don’t have to wear uniform, then you’re not in army).
- Now ofcourse there would be exceptional situation when army officer/jawan doesn’t need to wear uniform, for example during espionage mission behind the enemy lines. In that case you don’t have to wear uniform, but you’re still in the army.
- But keep in mind, while solving logical connective question under the “aptitude/reasoning” portion you don’t have to surgically dissect or nitpick the meaning every statement. Just “if 1=>2” then “~2=>~1”.
Demo Q: Only if: bored TV brother (CSAT 2012)
Examine the following statements:
- I watch TV only if I am bored
- I am never bored when I have my brother’s company.
- Whenever I go to the theatre I take my brother along.
Which one of the following conclusions is valid in the context of the above statements?
- If I am bored I watch TV
- If I am bored, I seek my brother’s company.
- If I am not with my brother, then I’ll watch TV.
- If I am not bored I do not watch TV.
Approach
First we’ll construct valid inferences from the question statements
Given Question Statement #1:
- Given =I watch TV only if I am bored
- This is not in standard format. So first exchange position
- Only if I’m bored (1), I watch TV(2)
- What is the valid inference? Just look at the formula table
- Only if 1=>2 then ~1=~2
- Valid inference= if I’m not bored, I do not watch TV.
- Look at the statements given in the answer choices, (D) matches. Therefore, final answer is (D).
Demo Q (If, then) Professor Headaches (CAT’98)
You’re given a statement, followed by four statements labeled A to D. Choose the ordered pair of statements where the first statement implies the second and two statements are logically consistent with the main statement.
Given statement: If I talk to my professors(1), then I didn’t need to take a pill for headache.(2)
Four Statements
- I talked to my professors
- I did not need to take a pill for headache
- I needed to take a pill for headache
- I did not talk to my professor.
Answer choices
- AB
- DC
- CD
- AB and CD
Approach
Given statement is in standard format already
| #1 | I talk to my professors |
| #2 | I didn’t need to take a pill for headache. |
Let’s classify the four statements
| Classification | Four statements |
| 1 |
|
| 2 |
|
| ~2 |
|
| ~1 |
|
Answer choice (i) AB
If you observe the answer choice (I): AB= I talked to my professors, I did not need to take a pill for headache. This is valid because if 1=>2 is already given in the question statement itself.
Answer choice (ii) DC
- I did not talk to my professor (~1), I needed to take a pill for headache (~2). Meaning ~1=>~2.
- This is invalid because as per our table, if 1=>2, then valid inference is ~2=>~1.
Answer choice (iii) CD
I needed to take pill for headache (~2), I did not talk to my professor (~1). Meaning ~2=>~1. This is valid as per our table. Therefore final answer is (IV) AB and CD
Demo Q: Either or: derailed/late train (CAT’97)
Given statement: either the train is late (1) or it has derailed (2)
Four statements
- Train is late = 1
- Train is not late = ~1
- Train is derailed =2
- Train is not derailed =~2
(^note: I’ve classified the statements in advance)
Answer choice
- AB
- DB
- CA
- BC
Approach
As per our table, the valid inferences for either or are
| ~2=>1 | If the train is not derailed, it is late. | DA |
| ~1=>2 | If the train is not late, it is derailed | BC |
Correct answer is (III): BC
For more articles on reasoning and aptitude, visit Mrunal.org/aptitude
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mrunal sir
SBI PO 2013 held this past sunday…. plzzz provide us with ANALYSIS of tht paper….. some starting questions were quite tuf and critical in reasoning….
Directions—(Q. 36-40) Study the following arrangements carefully and answer the questions given below—
Series I. MNLqd fuw2UFOKP6hs (14) SHV 7gc8RIE(13)xtk
Series II. azj14GJBopir5v9TQY(10) emn(11) DACby(12)xWZ
36. How many capital letters are in Series I and in Series II each of which is either followed by or preceded by the same positioned capital letter of English alphabet from the other end ?
(A) 4, 3
(B) 6, 2
(C) 8, 1
(D) 10, 0
explain it
http://books.google.co.in/books?id=4IlksDTr75YC&pg=PP11&lpg=PP11&dq=How+many+capital+letters+are+in+Series+I+and+in+Series+II+each+of+which+is+either+followed+by+or+preceded+by+the+same+positioned+capital+letter+of+English+alphabet+from+the+other+end+?&source=bl&ots=pTy7tgi27X&sig=yO1s6Mu7EYHJA3G_N_ir_PbkAog&hl=en&sa=X&ei=_fSBUZjsCYusrAejqYCgDg&ved=0CDIQ6AEwAA
number the series
1. from starting and
2. from backward (Exclude the numbers 2,6,14,7 etc in both countings).
You can number only Capital letters and just put dash in place of small letters.
Example first series 1 2 3 – – – – – 9 10 11 and so on.
When you complete numbering in both directions you ll find number pairs appearing in both the countings (9,10), (10, 11), (16,17), (17,18). This is the answer for Series I. You can do it for Series II in similar way.
Thanks a lot Mrunal….I was waiting for this for such a long time…u rock dude !!!!
Hi ,
First of all Mrunal can be pl suggest some source from where I can get more questions to practice as I can’t anything about this on net or any book (MKPandey/RSAggarwal).
Secondly I understand the method you are staying but there is problem in solving tose questions that involve more then 1 question statements. How to approach those? I am helpless so pl pl tell us how.
Example:
1. Whenever prices go up, farmers are affected.
2. Farmers are affected only if it does not rain.
3. It rains if there are clouds.
Conclusions:
1. Farmers are always affected by rain.
2. If it does not rain, farmers are affected.
3. Whenever there are clouds, prices go up.
4. If there are clouds, farmers are not affected.
So as you can see in this case we need to combine 2 statements together in order to get the conclusion. So I am not sure how to go with this..
Thanks
what is the answer. I think its 1. pls reply
Was waiting too! :) thanks thanks mrunal! Godbless
mrunal….plz see the correction
I watch TV only if I am bored
answer can be…
If I am not bored I do not watch TV.
If i am watching tv that means i am bored
If I am not watching Tv I am not bored
I feel this is what the diff between if and only if
symboilicaly
If(1)—->2
for
only if (1)(2)
if i am wrong enlighten me
only if (1)(2)
only if (1) arrow both side(2)
Please also post on how to solve questions asking to select two statements which both can be true but both cannot be false and another type like which both cannot be true but both can be false..
It will be of great help to us..
sir..
how to solve this question? If I quit school,then I’ll buy a car.If I get a god job offer,then i will quit school.
a)If i dont buy a car,then i didnt get a good job offer b)If i dont get a good job offer,then i wont buy a car c)If i buy a car,then i got a good job offer
Statements can be written as
If I get a good job offer, then I quit school
If I quit school, then I buy a car
From both the above statements, we can write
If I get a good job offer, then I buy a car.
Now, using this, we can come to the inference
If I don’t buy a car, then I didn’t get a good job offer.
@Anamika – Good doubt.
@Xerxes – Continuation to Anamika’s Question.
What if the question has 2 different statements.How do we solve ? For Ex.
If I get a good job offer, then I quit school.
If I join college , then I buy a car.
@Mrunal: In the bored TV brother Question from CSAT 2012 we have ignored the other 2 statements because there were no conditions in the statements or do we consider only the first statement with conditions to apply the table ??
Clarifications on this would be really helpful.
answer should be A
answer is (A)
I’ll buy a car.If I get a god job offer
JUST SOLVE WITH DYS
Are you sure? I think from this statement the only thing you can conclude is if I have a good job offer, I’ll buy a car not the other way around. Here the statement does not say that I’ll buy a car only if I get a good job offer. He might buy a car in other situations too and getting a good job offer is one of them.
will 200 marks in general category sufficient 2 clear prelims????
@love sandilya
actually nobody knows exact key other than upsc. some other things also play role ie. paper standard.
one more thing is it is based on relative performance. better than pondering over the cut-off, let’s concentrate on what ever you can do.
No, 220 around
Wait till UPSC declares its cut off.don’t get trapped in any speculations and rumours.Some say 210 was the cut off, some say 220-230,so don’t get disheartened and wait to hear from the horses mouth.
awesome article…
thanks a lot mrunal sir ! NOBODY can explain this stuff like you
Sir,
I have a doubt.what is nuclear triad?? in CST i read it as nuclear capability to strike by land,air and water.but on wikipedia i read it as a nuclear arsenal which consists of three components, traditionally strategic bombers, intercontinental ballistic missiles (ICBMs), and submarine-launched ballistic missiles (SLBMs).whatz true???
dear ajinkya……….if u take a closer look at ur statements u can solve ur doubt….obviously a country which has a bomber can make a nuclear strike by air, ICBM can be used to deliver nuclear bombs via the land route and SLBMs can be handy during a water based nuclear strike…………
It is same Strategic Bombers used in Air, Intercontinental Ballistic Missiles (ICBMs) from Surface or Land and Submarine-Launched Ballistic Missile (SLBMs) from Water. So in CST “Platfrom of Launch” is given to define it and in Wikipedia “Types of Missile used from these Platform or Area” are given.
Friends,
Does your UPSC eAdmit card have your’s signature below your photograph ?
plz do reply
nope…mine does not have signature in admit card
No, the admit card does not have our signature.
There is no provision of Sign there and hence shouldn’t be.
When u give prelims , u’ll know why ur sign had been taken.
Hey Manu bhai you sound suspicious :)
Is there anything regarding the sign that people who are giving the exam are not aware of? if so then please share it with us _/\_.
haha , no Bhai :)
Actually, we have to sign one paper there in which our “scanned” sign is already there. when u sign there , they tally ur Scanned sign and your present sign to check whether u are the same person or just another Kalmadi type person.
Jha jee… Wah jeee
Mrunal sir can u pls upload the s and t,kurukshetra and yojana archives like you did previous year…its a request…
Can u please make us understand the difference among Assumption, Inference and Conclusion for solving questions in comprehension and statement-assumption & statement-conclusion type ?
This is given in separate article..
Search it.
“Notice- Smoking is injurious to health.”
Assumption – Some people smoke. AND People have read this notice. (something which u assume from the statement.It may be that people dont smoke but if that was the case that notice would have been never there)
Inference – You may develop any specific disease if you smoke. OR Smoking causes Injury (something which can deduce from the statements but it should give proper evidence and not through a mere observation)
Conclusion – You can save your health by not smoking. (what u finally judge from the given statement but it Must FOLLOW from the given statements.)
I have given u a mere idea , you can do some problems on it to get a better hold.
Thank you manu ji
Most awaited article,Thank you.
Hi, I’m trying to decide between ALS and Vajiram Ravi for mains coaching for political science. I dont have much information on either of them. Can anyone help me choose between the two. Thanks
go with vajiram
Thanks a ton…
But i got some problem, plz help how to solve.???.
I remember her every time I see her photo.
given answer may be wrong ..
awesome boss , you r simply super
Please explain this question. I’ve tried it in ur method but i’m not able to get the answer… Qs:1.he writes whenever he is angry. 2.it is cloudy only if he is angry. 3.he is angry only if he is hungry. Options:A) he writes whenever he is hungry. B) he is hungry if he writes. C) he writes only if it is cloudy. D) whenever it is cloudy he writes.
As per the approach: converting the above statements in to standard formats. 1. Not 2=not 1 i.e. He dont write when he is not angry. 2. Not 1 = not 2 i.e. He is not angry it is not cloudy. 3. Not 1= not 2 i.e. He is not hungry he is not angry. After this im not able to correlate the above statements. Please explain. Thanks….
Hi Ahamed,
Second and third statements can be written as :
2) If it is cloudy >>He is angry
3) If he is angry >> he is hungry
and 1st statement can be written as
1) If(whenever) he is angry >> he writes
By 1) 2) 3) we can conclude if it is cloudy>> he is angry>> he writes . So according to me ans is D
Hey sumit, the answer is indeed D. Very nice explanation. Thanks a lot. I’ve some more questions like that. Ill try to find answer by myself if not ill upload it. If u can plz help. Thanks again…
Sure Ahamed,
thanks
Convert all 1,2,3 and A, B, C and D into Standard Format and get inference for them according to formula then see if inference for at least one of (1, 2, 3) matches to inference driven from A, B, C or D
Answer: A (It is same statement)
Na bhutoo na bhavishayat!!!!!!!!!!
Liked that
thanks
sir i tried hard to find tutorials on such questions but cudnt able to find…finally my wait is over…
thankyou sir
it is becoz of your articles i hav managed to continue my study in these last days..
munral sir i have been impressed by the yeomanry of yours.but are you a technocrat? or a humanities student or a science scholar. kindly give the reply.
PLEASE SOLVE THIS. STATEMENTS
1)He writes whenever he is angry.2)It is cloudy only if he is angry.3) He is angry only if he is hungry.
CONCLUSIONS
1)He writes whenever he is hungry.2)He is hungry if he writes.3)He writes only if it is cloudy.4)whenever it is cloudy,he writes.
Convert all 1,2,3 and A, B, C and D into Standard Format and get inference for them according to formula then see if inference for at least one of (1, 2, 3) matches to inference driven from A, B, C or D
Answer: A (It is same statement)
thx sir… u r one among such great artist who can make hardest thing to look simpler!!
A much awaited article. Thank you! :)
Sir pls refer the following question!
1.Only when book reads does river flow
2.if rever flows vocabulary improves
3.vocabulary improves only if computer cranks
Conclusion
a. computer cranks when book reads
b.if river flows computer cranks
c.River flows only if computer cranks
sir i’m confused with the b and c conclusions, both looks to similar . can u pls differentiate it.
could someone help me out in the above question??????
a is d answer
1.riverflow==>bookreads
2.riverflow==>vocabularyimproves
3vocab imp==>computercaranks
the possible outcome would be “riverflow ==>computercranks”
i feel option a gets no logic as ther is no relation b/t computer cranks and book reads.but if u see the b and c option , both option satisfies the outcome. could u get me????
Hi Parthi,
You are absolutely right. Both B and C are same conclusion and are right. Option A is wrong.
hmmm thank u sumit!!!!!
A Is the answer. It says COMPUTER DID OT CRANK====> BOOK WAS NOT READ.
Computer DID NOT crank===> Vocab DID NOT improve.
Vocab DID NOT improve====>River DOES NOT flow.
River DOES NOT flow====> Book WAS NOT read.
Hope you understood the explanation. If anythng wrong kindly reply.
ans is B AND C …..SURE
hmm thank u matt
answer is c only..
jst first try to convert all sentence in if .
if,river flow ===> book read
if,river flow ===> vocab
if,vocab==>comp cranck
now see the 3rd ans.
River flows only if computer cranks
means
if river flow==> comp cranck
i think now yo got your answer..
:):)
Sir you have recommended a book named Verbal Ability and Reading Comprehension for the CAT buy Arun Sharma (TMH), In this book page n.3.63 Logical Deduction. please solve five question from practice exercise from the method of your article which you named Logical Connectives. ( please solve I got two answer in many question)
@Mrunal,
In the “Demo Q: Only if: bored TV brother (CSAT 2012)” solving, you’ve considered only first statement. What about the other statements in the question?
@Mrunal,
In the “Demo Q: Only if: bored TV brother (CSAT 2012)” solving, you’ve considered only first statement. What about the other statements in the question?
Let me read it later and thank you first!
isi ka wait to bahut time se kar raha tha .. thanks mru bhai