Question

The Cartesian product \(A\times A\) has \(9\) elements and contains \((-1,0)\) and \((0,1)\). What is \(A\)?

Options

• \(\{-1,0,1,9\}\)

• \(\{-1,0\}\)

• \(\{-1,0,1\}\)

• \(\{0,1\}\)

Answer 1

Since \(n(A\times A)=9\), \(n(A)^2=9\), so \(n(A)=3\). The two given ordered pairs require \(-1\), \(0\), and \(1\) to belong to \(A\).