If set 𝑋 contains the elements
eight, four, six; set 𝑌 is equal to six, seven; and set 𝑍 is equal to seven, find
the Cartesian product of set 𝑋 and the intersection of set 𝑌 and 𝑍.
We recall that the Cartesian
product of two sets is the collection of all ordered pairs. The intersection of two sets is
those elements that occur in both sets, in this case in set 𝑌 and 𝑍. Set 𝑌 contains the elements six
and seven, whereas set 𝑍 only contains the number seven. This means that the only number
that appears in both sets is seven. The intersection of set 𝑌 and 𝑍
is equal to seven. We are told in the question that
set 𝑋 contains the numbers eight, four, and six.
We now need to find the Cartesian
product of these two sets. As our first value in the Cartesian
product is 𝑋, each of the elements of 𝑋 will be the first number in the ordered
pairs. Our first ordered pair is therefore
eight, seven. Next, we have four, seven. Finally, we have the ordered pair
six, seven. Each of our values in set 𝑋 has
now been matched with the value of seven in the set 𝑌 intersection 𝑍. The Cartesian product contains the
ordered pairs eight, seven; four, seven; and six, seven.