Question

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

Hint:

The inverse negates both the hypothesis and conclusion, while the contrapositive negates and swaps the hypothesis and conclusion.

Answer 1

Inverse of the statement: The inverse of a statement "If \( P \) then \( Q \)" is: \[ \text{If not } P, \text{ then not } Q. \] So, the inverse of the given statement "If \( x<y \), then \( x^2<y^2 \)" is: \[ \text{If } x \geq y, \text{ then } x^2 \geq y^2. \] Contrapositive of the statement: The contrapositive of a statement "If \( P \) then \( Q \)" is: \[ \text{If not } Q, \text{ then not } P. \] So, the contrapositive of the given statement "If \( x<y \), then \( x^2<y^2 \)" is: \[ \text{If } x^2 \geq y^2, \text{ then } x \geq y. \]