Question

What is the converse of the conditional statement?

If x is even, then x + 1 is odd.

If x is not even, then x + 1 is not odd.
If x + 1 is odd, then x is even.
If x + 1 is not odd, then x is not even.
If x is even, then x + 1 is not odd.

Answer 1

The answer is; ' if x + 1 is odd, then x is even.

A conditional statement like the one given above has two parts;

i) The hypothesis part which contains a clause with the word "if"

ii) The conclusion which contains a clause with the word "then"

From a conditional statement you can write three statements, that is:

i) A converse statement

A converse statement involves interchanging the order of conclusion with the hypothesis. In this way you start with the conclusion rather than the hypothesis of the initial statement.

ii) An inverse statement

Inverse statement involves the negation of both the hypothesis and the conclusion of the initial statement.

iii) A contrapositive statement

A contrapositive statement involves interchanging the hypothesis and the conclusion of an inverse statement of an initial statement.

Answer 2

If x + 1 is odd then x is even is the correct converse of the conditional statement that is known as contrapositive statement.

The start of the hypothesis of the question will begin with if while the conclusion part will be determined with a then.

In the contrapositive statement, you simply have to reverse the original statement.