Question

Let U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}, A = {1, 3, 5, 7, 9}, B = {2, 4, 6, 8, 10}, and C = {1, 2, 4, 5, 8, 9}. List the elements of each set.

Answer 1

`C\ n\ C^c = \{ \}`

`(A\ n\ C)^c = \{2,3,4,6,7,8,10\}`

`A\ u\ (B\ n\ C) = \{1, 2,3, 4,5, 7, 8,9\}`

Explanation:

Required

Determine

`C\ n\ C^c`

`(A\ n\ C)^c`

`A\ u\ (B\ n\ C)`

Solving
`C\ n\ C^c`

`C^c` implies that elements in U but not in C

Since

`C = \{1, 2, 4, 5, 8, 9\}`

`C^c = \{3, 6, 7, 10\}`

`C\ n\ C^c = \{1, 2, 4, 5, 8, 9\}\ n\ \{3, 6, 7, 10\}`

`C\ n\ C^c = \{ \}`

Because there's no intersection between both

Solving
`(A\ n\ C)^c`

First, we need to determine A n C

`A\ n\ C = \{1, 3, 5, 7, 9\}\ n\ \{1, 2, 4, 5, 8, 9\}`

`A\ n\ C = \{1, 5, 9\}`

`(A\ n\ C)^c = (\{1, 5, 9\})^c`

`(A\ n\ C)^c = \{2,3,4,6,7,8,10\}`

Solving
`A\ u\ (B\ n\ C)`

First, we need to determine B n C

`B\ n\ C = \{2, 4, 6, 8, 10\}\ n\ \{1, 2, 4, 5, 8, 9\}`

`B\ n\ C = \{2, 4, 8\}`

So:

`A\ u\ (B\ n\ C) = \{1, 3, 5, 7, 9\}\ u\ \{2,4,8\}`

`A\ u\ (B\ n\ C) = \{1, 2,3, 4,5, 7, 8,9\}`