Chapter 5.4, Problem 4CYP

To determine

Prove with the help of indirect proof method.

Answer to Problem 4CYP

Proved that square of an odd integer is odd.

Explanation of Solution

Given information:

If square of an integer is odd then integet is odd.

Calculation:

Consider if square of an integer is odd then integet is odd,

Prove,if $x$ is an odd inter then $x^2$ is also odd.

As per indirect proof, $x=2k+1$ where $k$ is an integer,

Then,

  $\begin{array}{l}{x}^2=2k+1\\ {\left(2k+1\right)}^2=2k+1\end{array}$

Hence, proved that square of an odd integer is odd. $2k+1$ is odd because $k$ is an integer.