Video Transcript
Use the Venn diagram to find the complement of 𝑋 union 𝑌.
Well, the first thing we want to do in this question is take a look at some of the notation that we’re using. So here, we’ve got the complement of 𝑋 union 𝑌. So first of all, what we can take a look at is the bit in the middle, this U shape. So what does this mean? Well, this means union. So 𝑋 union 𝑌 means 𝑋 or 𝑌. And if we have a bar above the letter, so here we’ve got 𝑋 bar, then what this means is the complement of 𝑋. So what this means is that it’s not 𝑋. So it’ll be all the values that are not in the set 𝑋.
So therefore, if we look at the notation we’ve got which is the complement of 𝑋 union 𝑌, then what this means is we’re looking for the values or the set of values that are not in the set 𝑋 or y. So therefore, if we take a look at our Venn diagram, we can see the set 𝑋 or 𝑌 or 𝑋 union 𝑌 is the set one, four, five, nine. So therefore, the complement of 𝑋 union 𝑌 or the set of values that are not in 𝑋 union 𝑌 are six, seven, and eight.
