Question

Let \(A=\{1,2,3\}\), \(B=\{3,4\}\), and \(C=\{4,5,6\}\). What is \((A\times B)\cap(A\times C)\)?

Options

• \(\{(1,4),(2,4),(3,4)\}\)

• \(\{(1,3),(2,3),(3,3)\}\)

• \(\{(1,3),(1,4),(1,5),(1,6)\}\)

• \(\{(1,5),(2,5),(3,5)\}\)

Answer 1

An ordered pair must occur in both Cartesian products. The only common second component of \(B\) and \(C\) is \(4\), with first component from \(A\).