Question

Let U = {1, 2, 3, 4, 5, 6, 7, 8}, A = {4, 8, 6}, B = {1, 2, 5, 4}, and C = {3, 5, 1}. Find the following. (Enter your answers as a comma-separated list. Enter EMPTY for the empty set.) A ∩ (B ∩ C)

Answer 1

`A\capB\capC` = EMPTY

Explanation:

The intersection of two sets is the set that contains every element that is in both of those sets.

Because of the (), initially we are going to solve
`B\capC`.

B = {1, 2, 5, 4}

C = {3, 5, 1}

The elements that are in both B and C are 1 and 5, so:

`B \cap C = \left\{1,5\right\}`

Now we do
`A\capB\capC`

A = {4, 8, 6}

`B \cap C = \left\{1,5\right\}`

There are no elements that are in each of those sets, so the result of the intersection of these sets is the empty set;

`A\capB\capC` = EMPTY