Use the Venn diagram below to find
the Cartesian product of 𝑋 and 𝑍.
The multiplication or times sign in
the question means the Cartesian product. This is a collection of all ordered
pairs. We can begin by writing the
elements of set 𝑋, 𝑌, and 𝑍. Set 𝑋 just contains one element,
the number six. Set 𝑌 contains the elements four
and nine. Set 𝑍 contains the elements five,
three, and four. Five and three appear in just set
𝑍, whereas four appears in the intersection of set 𝑍 and set 𝑌. We’re interested in the Cartesian
product of set 𝑋 and set 𝑍.
As the first letter in our
Cartesian product is 𝑋, the elements in this set will be the first number in our
ordered pairs. The elements of set 𝑍 will be the
second number. Our first ordered pair is therefore
six, five. Next, we have six, three, the six
from set 𝑋 and the three from set 𝑍. Finally, we have the ordered pair
six, four. Each of the elements in set 𝑍 has
now been matched with the six in set 𝑋. The Cartesian product of set 𝑋 and
set 𝑍 is six, five; six, three; and six, four.