Question

A(1,3,5, 7,9}, B {0,1,2,3,4,5,6, 7,8,9} be the universal set and let A (0,2,4,6,8}, and C {2,3,5,7}. List the elements of the following sets 1.) Let U (a) An B (b) C\B (c) AU (Bnc)

Answer 1

a)
`A \cap B = A`

b)
`C - B = {}`

c)
`A \cup (B \cap C) = A \cup C = \left\{0,2,3,4,5,6,7,8\right\}`

Explanation:

We have the following universal set

`B = \left\{0,1,2,3,4,5,6, 7,8,9\right\}`

We also have these following sets:

`A = \left\{0,2,4,6,8\right\}`

`B = \left\{2,3,5,7\right\}`

a)
`A \cap B`

`A \cap B` is the set of elements that belong to both A and B.

B is the universal set, so:

`A \cap B = A`

b)
`C - B`

`C - B` is the set with all elements that belong to C and do not belong to B.

B is the universal set, so:

`C - B =\left\{\right\}`

c)
`A \cup (B \cap C)`

Because of parenthesis,
`B \cap C` takes precedence.

In a), I explained the
`\cap` operation.

B is the universal set, so:

`B \cap C = C`

Now we have
`A \cup (B \cap C) = A \cup C`

`A \cup C` is the set formed by the elements that belong to at least one of A or C.

So:

`A \cup (B \cap C) = A \cup C = \left\{0,2,3,4,5,6,7,8\right\}`