Question Video: Finding the Cartesian Product of the Difference and Union of Sets given Their Venn Diagram Mathematics

Video Transcript

Determine 𝑍 minus 𝑌 times 𝑋 ∪ 𝑌 using the Venn diagram below.

First of all, 𝑍 minus 𝑌 will be everything in the set 𝑍 that’s not in 𝑌. The number seven is part of 𝑍, but it is also part of 𝑌. We won’t take this value. Three and eight are part of 𝑍, but not part of 𝑌. The set of 𝑍 minus 𝑌 is the set three, eight.

Next, we need the set of 𝑋 ∪ 𝑌: everything in 𝑋 and everything in 𝑌 four, seven, and nine. After that, we want to multiply these sets together: three, eight times four, seven, nine. First, we have the ordered pair three, four, then three, seven, and then three, nine. Following that same pattern, eight, four; eight, seven; eight, nine.

We write these ordered pairs in set notation with brackets and then we list out all the ordered pairs. Now, we can list the ordered pairs in any order as long as you’re not changing what is inside the ordered pair. For example, I could switch these two ordered pairs and have three, seven first in the set and then three, four second. But I could not change the ordered pair three, seven to say seven, three.

Now that we’re clear on all of that, here are our six ordered pairs: three, four; three, seven; three, nine; eight, four; eight, seven; eight, nine.