Given that the set of elements zero, four, and 𝑎 is equal to the set of elements four, 12, 𝑏 is equal to the set of elements zero, 12, 𝑐, find 𝑎, 𝑏, and 𝑐.
Since the sets are equal, we know that the same three elements belong to each set. So let’s begin by color-coding the numbers in the sets. The zeroes can be pink. The fours can be green. And the 12s can be black. So looking at the first set, which color is it missing? It’s missing the color black. And 12s are black. So 𝑎 must be 12.
Now, for the second set, what color is it missing? Pink. Therefore, 𝑏 must be zero. And in the last set, the color that it’s missing is green. So that must mean that 𝑐 is equal to four. And now, we’ve solved for 𝑎, 𝑏, and 𝑐.
So our final answer will be that 𝑎 is equal to 12, 𝑏 is equal to zero, and 𝑐 is equal to four.