Question Video: Finding a Set given Its Cartesian Product with Another Set

If 𝑋 Γ— π‘Œ = {(8, 0), (8, 6), (1, 0), (1,6), (3, 0), (3, 6)}, find 𝑋.

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Video Transcript

If the Cartesian product of set 𝑋 and set π‘Œ is equal to the set of ordered pairs eight, zero; eight, six; one, zero; one, six; three, zero; three, six, find set 𝑋.

The notation in the question denotes the Cartesian product. This is the set of all ordered pairs. As the first value of our Cartesian product is 𝑋, the first values in our ordered pairs must all be contained in set 𝑋. Likewise, the second values in the ordered pairs must be contained in set π‘Œ. As there are three different 𝑋-values in our set of ordered pairs, set 𝑋 will contain these three values. They’re the numbers eight, one, and three. There are two different π‘Œ-values, the numbers zero and six. As we are only interested in set 𝑋, the correct answer is eight, one, and three.

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