Question Video: Finding the Cartesian Product of Sets Using a Given Venn Diagram Mathematics

Use the Venn diagram below to find 𝑋 Γ— 𝑍.

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Video Transcript

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, π‘Œ, and 𝑍. Set 𝑋 just contains one element, the number six. Set π‘Œ 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 π‘Œ. 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.

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