LOGICAL CONNECTIVES

Introduction

Suppose we have a statement like: If I talk to my professor then I don't need to take a pill.>

Then the above statement has two parts:

Part A: I talk to my professor

Part B: I don't need to take a pill.

Part A and Part B are connected by logical connective in this case is If .... then and we have to find out the equivalent inference.

Rule 1: If .... then

If A then B is equivalent to If not B then not A

E.g: If you are in army then you wear a uniform.

A. Here A = you are in army; B = you wear a uniform; Now applying above rule we know If A then B is same as If not B then not A.

So we get inference:If you don't wear a uniform then you are not in the army.

Rule 2: When

When A then B is same as inference when not B then not A

E.g: I am never bored when I have my brother.

Ans. Here we have to rearrange the statement in the form when A then B; so we get when I have my brother, I am never bored.

Inference: When I am bored, I don't have my brother.

Rule 3: Whenever

Whenever A then B is same as inference when not B then not A

E.g: whenever I go to the theater, I take my brother.

Ans. Here we have the statement in the form whenever A then B; so we get:

Inference: If I don't take my brother then I don't go to the theater.

Rule 4: Everytime

Everytime A then B is same as inference when not B then not A

E.g: Everytime there are heavy rains, the trains are late.

Ans. Here we have the statement in the form Everytime A then B; so we get:

Inference: If the trains are not late then there are no heavy rains.

Rule 5: Only If

Only if A then B is same as inference If not A then not B.

E.g: Federer shall lose only if Nadal shall play.

Ans. Here we have the statement in the form B only if A; so we have to convert it of the form Only if A then B:

"Only if Nadal shall play, Federer shall lose".

Rule 6: Unless

Unless A then B is same as inference If not B then A.

E.g: Unless the Banks bring down lending rates, Business shall remain stagnant.

Ans. Here we have the statement in the form Unless A then B; so we have the following statement:
"Unless the Banks bring down lending rates, ----> Part A

Business shall remain stagnant". -----> Part B

Inference: If business should not remain stagnant then banks must bring down lending rates.

Rule 7: Otherwise

A otherwise B is same as inference If not B then A.

E.g: You should study otherwise you shall fail.

Ans. Here we have the statement in the form A otherwise B; so we have the following statement:
"You should study, ----> Part A

Otherwise -----> logical connective

You shall fail". -----> Part B

Inference: If you don't want to fail you should study.

Rule 8: Either .... Or

Either A or B is same as inference If not B then A. OR
If not A then B

E.g: Either train is late or It has derailed.

Ans. Here we have the statement in the form Either A or B; so we have the following statement:
"Either train is late, ----> Part A

or -----> logical connective

It has derailed". -----> Part B

Inference: If train has not derailed then train is late. OR

If train is not late then it has derailed.