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

Question

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.

Philoid · Accepted Answer

Let a = – 1 & b = 1

Now,

a² = (– 1)² = 1

b² = (1)² = 1

Since a² = b² = 1

But a ≠ b

⇒ – 1 ≠ 1

Hence the given statement is not true.

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