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

Question Video: Finding the Cartesian Product of Sets Using a Given Venn Diagram Mathematics • Third Year of Preparatory School

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Use the Venn diagram below to find π Γ π.

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Video Transcript

Use the Venn diagram below to find the Cartesian product of π and π.

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 π, π, and π. Set π just contains one element, the number six. Set π contains the elements four and nine. Set π contains the elements five, three, and four. Five and three appear in just set π, whereas four appears in the intersection of set π and set π. Weβre interested in the Cartesian product of set π and set π.

As the first letter in our Cartesian product is π, the elements in this set will be the first number in our ordered pairs. The elements of set π will be the second number. Our first ordered pair is therefore six, five. Next, we have six, three, the six from set π and the three from set π. Finally, we have the ordered pair six, four. Each of the elements in set π has now been matched with the six in set π. The Cartesian product of set π and set π is six, five; six, three; and six, four.

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