Let U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} A = {1, 2, 4, 6, 8, 10} B = {1, 3, 5, 7, 8, 9}

Question

Find:

(a) A'

(b) B'

(c) A' ∪ B'

(d) A' ∩ B'

(e) (A ∪ B)'

Answer 1

A and B are subsets of U.

 

 

(a) A' = {3, 5, 7, 9} since these numbers in U are not in A.

(b) B' = {2, 4, 6, 10} since these numbers in U are not in B.

 

(c) A' ∪ B' = {2, 3, 4, 5, 6, 7, 9, 10} from A' and B' above.

 

(d) A' ∩ B' = {∅} because there are no numbers common to A' and B'.

 

(e) (A ∪ B)' = {∅} since A ∪ B = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} = U.