Consider the statement :
q : For any real numbers a and b, a² = b²⇒ a = b

By giving a counter-example, prove that q is false.

Question

Consider the statement : q : For any real numbers a and b, a 2 = b 2 ⇒ a = b By giving a counter-example, prove that q is false.

Philoid · Accepted Answer

Let us take the numbers a= +5 and b= -5.

a² = (+5)² = 25

b² = (-5)² = 25

∴ a² = b²

But, +5 ≠ -5 ,thus a ≠ b.

∴ q is false.

Consider the statement :q : For any real numbers a and b, a2 = b2⇒ a = bBy giving a counter-example, prove that q is false.