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.
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.
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.
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.
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.
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".
Inference: If Nadal shall not play then Federer shall not lose.
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.
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.
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.