Question

Write inverse and contrapositive of the following statement: If \( x<y \), then \( x^2<y^2 \).

Hint:

Inverse negates hypothesis and conclusion; contrapositive negates and swaps them.

Answer 1

Given statement: If \( p \): \( x<y \), then \( q \): \( x^2<y^2 \).
Inverse: If \( \neg p \), then \( \neg q \): If \( x \geq y \), then \( x^2 \geq y^2 \).
Contrapositive: If \( \neg q \), then \( \neg p \): If \( x^2 \geq y^2 \), then \( x \geq y \).
Note: The statement assumes \( x, y \) are positive real numbers for \( x^2<y^2 \) to hold, as counterexamples exist (e.g., \( x = -2, y = 1 \)).