Question

If U = {−1, 0, 1, 14, 15, 16}, A = {1, 14, 16}, and B = {−1, 0, 14} find the following. (Enter your answers as a comma-separated list.)

(a)
A'




(b)
B'




(c)
(A ∪ B)'





(d)
(A ∩ B)'

Answer 1

Explanation:

A'

If A is subset of a given set U, then A' (the complement of a set A) is the set of elements in U but not in A.

A ∪ B

The union of A and B is the set of all things that are in A or B.

A ∩ B

The intersection A and B is the set of all things that are in both A and B.

U = {-1, 0, 1, 14, 15, 16}

A = {1, 14, 16}

B = {-1, 0, 14}

(a) A' = {-1, 0, 15}

(b) B' = {1, 15, 16}

(c) (A ∪ B)'

A ∪ B = {-1, 0, 1, 14, 16}

(A ∪ B)' = {15}

(d) (A ∩ B)'

A ∩ B = {14}

(A ∩ B)' = {-1, 0, 1, 15, 16}