Question

Write true $\left(T\right)$ or false $\left(F\right)$ for the following statements:
For an integer $a,a^3$ is always greater than $a^2$

Answer 1

Step: State true or false

Given statement: For an integer $a,a^3$ is always greater than $a^2$

Consider the value: $a=-2$
$\Rightarrow a^2=(-2{)}^2=-2\times -2=4$

$\Rightarrow a^3=(-2{)}^3=-2\times -2\times -2=-8$

Clearly, $-8<4$

$\Rightarrow a^3<a^2$

Therefore, the given statement does not hold true for all values of $a.$

Hence, the given statement is false.