Q.Write the contrapositive of the following statement:

For an implication "if $p$, then $q$" (written $p \Rightarrow q$), the contrapositive is "if $\sim q$, then $\sim p$" ($\sim q \Rightarrow \sim p$). It is logically equivalent to the original statement.

1. $p$: a number is divisible by 9; $q$: it is divisible by 3. Contrapositive: "If a number is not divisible by 3, then it is not divisible by 9."
2. $p$: you are born in India; $q$: you are a citizen of India. Contrapositive: "If you are not a citizen of India, then you are not born in India."
3. $p$: a triangle is equilateral; $q$: it is isosceles. Contrapositive: "If a triangle is not isosceles, then it is not equilateral."
   ✓Final answer

   (i) If a number is not divisible by 3, then it is not divisible by 9. (ii) If you are not a citizen of India, then you are not born in India. (iii) If a triangle is not isosceles, it is not equilateral.

Identify the hypothesis $p$ and conclusion $q$ of "if $p$ then $q$". Negate each ($\sim p$, $\sim q$), then write "if $\sim q$, then $\sim p$" — the negated conclusion becomes the new hypothesis, and the negated hypothesis becomes the new conclusion.

• Confusing the contrapositive with the converse — the contrapositive must both swap and negate, not just swap.
• Negating only one of the two parts.