Q.Write the converse of the following statements.

For "if $p$, then $q$", the converse is "if $q$, then $p$" — obtained by simply interchanging the hypothesis and conclusion, with no negation involved.

1. $p$: n is even; $q$: n$^2$ is even. Converse: "If n$^2$ is even, then n is even."
2. $p$: you do all the exercises in the book; $q$: you get an A grade in the class. Converse: "If you get an A grade in the class, then you do all the exercises in the book."
3. $p$: two integers a and b are such that a > b; $q$: a − b is always a positive integer. Converse: "If a − b is always a positive integer, then a > b."
   ✓Final answer

   (i) If n$^2$ is even, then n is even. (ii) If you get an A grade, then you did all the exercises. (iii) If a − b is a positive integer, then a > b.

Identify $p$ and $q$ in "if $p$, then $q$", then simply write "if $q$, then $p$" — swap the two clauses; do not negate anything (that would give the contrapositive/inverse instead).

• Accidentally negating one clause while swapping, producing the inverse or contrapositive instead of the converse.
• Assuming the converse is automatically true just because the original statement is true — converse truth must be checked separately.