Question

Which of the following statements is the inverse of “If it rains, then I do not go fishing”?
(A) If I go fishing, then it does not rain
(B) If I do not go fishing, then it rains
(C) If it does not rain, then I go fishing
(D) None of these

Answer 1

Hint: We are given a statement and we are asked to write the statement’s inverse. We will begin by breaking the given statement into two phrases, one will consist of the reason, which is, ‘If it rains…’ and the next part will consist of the assertion, which is, ‘..then I do not go fishing’. Inverse of a statement would mean negation of the reason and the assertion as well in the order – reason followed by assertion. Hence, we will have the inverse of the given statement.

Complete step by step answer:
According to the given question, we are given a statement and we are asked in the question to write the converse of this given statement.
The statement that we have is,
“If it rains, then I do not go fishing”
Let us assume,
p = If it rain
q = then I do not go fishing
Here, we have decomposed the given statement into two parts, the first part ‘p’ is the reason and the second part ‘q’ is the assertion which depends on the reason.
The symbolic representation of the given statement is,
\[p\to q\]
We have to write the converse statement of this given statement, the symbolic representation of converse statement is,
\[\sim p \to \sim q\]
The tilde sign (\[\sim\]) is used to denote negation. So, we will write the negative of the given statements wherever applicable.
So, we have,
Inverse: ‘’If it does not rain, then I go fishing’’

So, the correct answer is “Option C”.

Note: Along with inverse, we also have two other types of statement conversions which are, converse and contrapositive.
Converse (\[q\to p\]) of the given statement is: “If I do not go fishing, then it rains’’
And the contrapositive (\[\sim q \to \sim p\]) of the given statement is: “If I go fishing, then it does not rain”
These statements have very minute differences but that makes all the difference. Be watchful and do not get confused while carrying out the conversions.