Question

For two non-empty sets \(A\) and \(B\), which expression gives their Cartesian product?

Options

• \(A \times B=\{a,b:a\in A\cup B\}\)

• \(A \times B=\{(a,b):a\in B,\ b\in A\}\)

• \(A \times B=\{a:b\in A\cap B\}\)

• \(A \times B=\{(a,b):a\in A,\ b\in B\}\)

Answer 1

The Cartesian product is the set of all ordered pairs whose first component belongs to \(A\) and second component belongs to \(B\). The order of the two sets determines the order of components.