If 𝑋 is the set containing the number nine and 𝑌 is the set containing the numbers two and six, find the Cartesian product of 𝑋 and 𝑌.
We begin by recalling that the Cartesian product of two sets 𝐴 and 𝐵 is the collection of all ordered pairs 𝑥, 𝑦, where 𝑥 is an element of 𝐴 and 𝑦 is an element of 𝐵.
In this question, we’re given two sets 𝑋 and 𝑌. As there is only one element in set 𝑋, we need to match this with each of the elements in set 𝑌. Our first ordered pair is nine, two. This contains the element nine from set 𝑋 and the element two from set 𝑌. The second and final ordered pair is nine, six.
The Cartesian product of set 𝑋 and set 𝑌 is the set containing two ordered pairs nine, two and nine, six.