Show that the statement “For any real numbers a and b, a$^2$ = b$^2$ implies that a = b” is not true by giving a counter-example.

Show that the statement “For any real numbers a and b, a² = b² implies that a = b” is not true by giving a cou

Exercises · Q15

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Claim to disprove: "For any real numbers a and b, $a^2 = b^2$ implies that $a = b$ ."

To disprove a universal implication, one counter-example suffices — a pair (a, b) satisfying the hypothesis ( $a^2=b^2$ ) but not the conclusion ( $a=b$ ).

Let $a = 2$ and $b = -2$ .

Then $a^2 = 2^2 = 4$ and $b^2 = (-2)^2 = 4$ , so $a^2 = b^2$ holds.

But $a = 2 \ne -2 = b$ , so $a = b$ fails. …

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Q.Show that the statement “For any real numbers a and b, a $^2$ = b $^2$ implies that a = b” is not true by giving a counter-example.

Concept understanding — Counter-Examples

Q.Show that the statement “For any real numbers a and b, a2^22 = b2^22 implies that a = b” is not true by giving a counter-example.

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Q.Show that the statement “For any real numbers a and b, a $^2$ = b $^2$ implies that a = b” is not true by giving a counter-example.

Unlock everything free for 14 days