Question

If A = {–1, 1}, find A × A × A.

Answer 1

It is known that for any non-empty set A, A × A × A is defined as

A × A × A = {(a, b, c): a, b, c ∈ A}

It is given that A = {–1, 1}

∴ A × A = {- 1, 1} × {- 1, 1}

= {(- 1, – 1), (- 1, 1), (1, – 1), (1, 1)}

A × A × A = {- 1, 1} × {(-1, – 1), (- 1, 1), (1, – 1), (1, 1)}

= {(-1, – 1, – 1), (-1, – 1, 1), (- 1, 1, – 1), (-1, 1, 1), (1, – 1, – 1), (1, – 1, 1), (1, 1, -1), (1, 1, 1)}.