Question

U={1, 2, 3, 5, 7, 8)

B={1, 3, 7,8)
C={1,2}
Find the following sets.
Write your answer in roster form or as Ø.
(a) BUC' =
(b) (BOC)' =

Answer 1

a)
`B \cup C'=\{1,3,5,7,8\}`

b)
`(B \cup C)'=\{5\}`

Problem:

U={1, 2, 3, 5, 7, 8)

B={1, 3, 7,8)

C={1,2}

Find the following sets.

Write your answer in roster form or as Ø.

(a) BUC' =

(b) (BUC)' =

Explanation:

a)

We will need to find
`C'`.

`C'` is the elements in the universe
`U` that aren't in
`C`.

`U=\{1,2,3,5,7,8\}`

`C=\{1,2\}`

So
`C'=\{3,5,7,8\}`.

`B \cup C'`

`\{1,3,7,8\} \cup\{3,5,7,8\}`

union means it is in either/or so we have:

`\{1,3,5,7,8\}`

b)

We need to find
`B\cup C` first.

`B\cup C`

`\{1,3,7,8\}\cup \{1,2\}`

`\{1,2,3,7,8\}`

So now
`(B \cup C)'` means we are going to have the elements in the universe that aren't in
`B \cup C`:

`U=\{1,2,3,5,7,8\}`

`B\cup C=\{1,2,3,7,8\}`

`(B \cup C)'=\{5\}`