[Reasoning] Logical Connectives (if, unless, either or) for CSAT, CAT shortcuts formulas approach explained
 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).