 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 1^{st} happens then 2^{nd} happens”, in such situation, the only valid inference is “if 2^{nd} did not happen then 1^{st} 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 rewrite 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
198 Comments on “[Reasoning] Logical Connectives (if, unless, either or) for CSAT, CAT shortcuts formulas approach explained”
Sir,
kindly elaborate the negation of a statement…
Directions: Each question below consists of a main statement followed by four numbered statements. From the numbered statements, select the one that logically follows the main statement.
q1> Unless Sangeeta’s boss sanctions her leave and books the tickets, Sangeeta cannot go home for diwali.
a>Sangeeta is going home for diwali, hence, her boss booked her tickets but did not sanction leave.
b>Sangeeta is going home for dipawali,implies that her boss sanctioned leave but the tickets are not booked.
c>Sangeeta’s ticket was not booked implies, she is not going home for diwali.
d>More than one of the above.
Can you please explain me these type of questions with this example and if possible some other examples too??
Is it necessary to take coaching for REASONING IN CSAT?
Why are 1=> ~2 and 2=>~1 incorrect inferences in “Either/Or” questions? If one happens, the other doesn’t, since it is ‘either this, or that’ right? I am not able to understand the logic behind why it is incorrect. Someone please help if possible!
In either/or any one condition need to be fulfilled for the desired outcome. If cond. 1 is false, then cond2 needs to be true and vice versa.
Either RaGa will be PM or Namo.
Not Raga>Namo
Not Namo > Raga
nice article on logical deduction very easy to understand via this article.. thanku sir.:)
Mrunal u rock bro . Lovely article
Thanks a lot, Mrunal. This is what I needed! So clearly explained.
Hi there
Can you help me on this…
Qwhenever pollution is on the rise,vehicles will be stopped and their emission level eill be checked.
A)vehicles are not stopped or their emission level are not checked, means that the pollution is not on the rise.
B)if vehicles are not stopped but i pollution is on the rise,then emission levelslevel of vehiclesfear will definitelybe be checked.
C)if vehicles are stopped and their emission levels are not checked, it means that the pollution is not on rise.
D)both a and c
E)both b and a
AnswerD bith a and c
explain why
In a, effect 1is vehicle not stopping and effect 2 is emission level not being checked thus when both effects arent happening then cause isnt happening.
in c, vehicles are stopped i.e effect 1 has happened but emission level isnt checked thus the entire effect doesnt sum up the cause therefore pollution will not be on the rise.
what if the logical connective word is “provided”. for example, Martina wins the tournament provided she plays the final.
(a) Martina played the final
(b) Martina won the tournament
(c) Martina did not win the tournament
(d) Martina did not play the final.
Here the answer given is “ba”. but any of your explanation does not apply here. How to solve this kind of questions?
The same doubt !!!
Please help with the below question
Martina wins the tournament provided she plays the final.
A) Martina played the final.
B) Martina won the tournament.
C) Martina did not win the tournament.
D) Martina did not play the final.
Options:
a) AB b) BA c) CD d) AC
Ans given, option b
Also please tell what “provided” means in this statement.
Thanks,
Sheetal