If the Cartesian product of set 𝑋
and set 𝑌 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 𝑌. 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 𝑌-values,
the numbers zero and six. As we are only interested in set
𝑋, the correct answer is eight, one, and three.