Question Video: Finding the Cartesian Product of Two Given Sets Mathematics

If 𝑋 = {9} and π‘Œ = {2, 6}, find 𝑋 Γ— π‘Œ.

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Video Transcript

If 𝑋 is the set containing the number nine and π‘Œ is the set containing the numbers two and six, find the Cartesian product of 𝑋 and π‘Œ.

We begin by recalling that the Cartesian product of two sets 𝐴 and 𝐡 is the collection of all ordered pairs π‘₯, 𝑦, where π‘₯ is an element of 𝐴 and 𝑦 is an element of 𝐡.

In this question, we’re given two sets 𝑋 and π‘Œ. As there is only one element in set 𝑋, we need to match this with each of the elements in set π‘Œ. Our first ordered pair is nine, two. This contains the element nine from set 𝑋 and the element two from set π‘Œ. The second and final ordered pair is nine, six.

The Cartesian product of set 𝑋 and set π‘Œ is the set containing two ordered pairs nine, two and nine, six.

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