Question

Statement the converse and contrapositive of each of the following statements:
If you live in Delhi, then you have winter clothes.

Answer 1

Hint: We use the concepts of conditional statements which are in the form “if p, then q”, divide the hypothesis and conclusion of the statement and write the converse and contrapositive using their respective patterns.
* Converse of a condition statement “If p, then q” is “If q, then p”.
* Contrapositive of a condition statement “If p, then q” is “If not q, then not p”.

Complete step-by-step answer:
We are given the conditional statement of the form “If p, then q”.
Since we know a conditional statement has two parts, Hypothesis (denoted by p) and Conclusion (denoted by q).
We write the hypothesis and conclusion of this statement separately.
Looking at the statement “If you live in Delhi, then you have winter clothes”
Hypothesis is “You live in Delhi.” (p)
Conclusion is “You have winter clothes.” (q)
First we write the converse of the statement which is of the form “If q, then p”.
Writing the hypothesis in place of p and conclusion in place of q, we can write the converse of statement “If you live in Delhi, then you have winter clothes” as
“If you have winter clothes, then you live in Delhi.”
Now we find the contrapositive of the statement which is of the form “If not q, then not p”.
First we write the statements as ‘not p’ and ‘not q’.
‘not p’ is “You don’t live in Delhi.”
‘not q’ is “You don’t have winter clothes.”
Writing the hypothesis in place of p and conclusion in place of q, we can write the contrapositive of statement “If you live in Delhi, then you have winter clothes” as
“If you don’t have winter clothes, then you don’t live in Delhi.”
Therefore, the converse of the statement is “If you have winter clothes, then you live in Delhi.” And contrapositive of the statement is “If you don’t have winter clothes, then you don’t live in Delhi.”

Note: Students are likely to get confused with not p and not q part as they might try to write the word not in the statement but that is not completely right in all statements as here if we wrote “If not you have winter clothes, then not you live in Delhi” which will be wrong, by not p and not q we mean taking negation of the hypothesis and conclusion.