Find 𝐴 intersection 𝐶 using the Venn diagram.
First, we need to know this little upside-down ⋃. This symbol — the intersection symbol — tells us that we’re looking for values found in both 𝐴 and 𝐶. The space here between 𝐴 and 𝐵 with the numbers 11 and six is the intersection of 𝐴 and 𝐵. The numbers 11 and six are found in set 𝐴 and in set 𝐵. The numbers 10 and eight are the intersection of 𝐵 and 𝐶. 10 and eight are found both in set 𝐵 and in set 𝐶. And we’re trying to determine are there any values that are found in set 𝐴 and in set 𝐶.
Let’s list out the values of set 𝐴. Set 𝐴 is four, five, six, nine, 11. We can do the same thing for set 𝐶 — set 𝐶: zero, two, seven, eight, and 10. Now, is there any number that’s found in both 𝐴 and 𝐶? 𝐴 and 𝐶 don’t share any values. When two sets do not share any values, their intersection is called the empty set. We also might call this the null set.
The intersection of set 𝐴 and set 𝐶 is the empty set.