Decide whether the statement is true or false.
-$\text { For every real number } p , p ^ { 2 } \text { is positive and } p

Question

Decide whether the statement is true or false.
-$\text { For every real number } p , p ^ { 2 } \text { is positive and } p < p ^ { 2 } \text {. }$

Quizplus · Accepted Answer

For every real number $p$, $p^2$ is non-negative (not necessarily positive), and $p < p^2$ is not true for all real numbers, especially for $0$ and negative numbers. $p^2$ is only positive for non-zero $p$, and $p < p^2$ does not hold for $0$ (since $0^2 = 0$) or for numbers in the interval $(-1, 1)$ excluding $0$, where $p^2 < p$ if $p > 0$ and $p^2 > p$ if $p < 0$.

Decide Whether the Statement Is True or False For every real number p,p2 is positive and p<p2. \text { For every real number } p , p ^ { 2 } \text { is positive and } p < p ^ { 2 } \text {. } For every real number p,p2 is positive and p<p2.

Decide Whether the Statement Is True or False $\text { For every real number } p , p ^ { 2 } \text { is positive and } p < p ^ { 2 } \text {. }$