Let A = {1, 3, 6, 8, 9} B = {2, 5, 6, 7, 8} C = {1, 4, 6, 7, 8, 9} and D = {1,2}

Calculate (A∪B) ∩C

Calculate P (D), i. e., power set

Is (A ∩ B) ⊆C? Why or why not?

What is (B ∩ C) * {1,2}?

Answer with Step-by-step explanation:

Let A = {1, 3, 6, 8, 9}

B = {2, 5, 6, 7, 8}

C = {1, 4, 6, 7, 8, 9}

and D = {1,2}

Calculate (A∪B) ∩C

A∪B={1,2,3,5,6,7,8,9} (union of two sets is the set of element which are in any one of the two sets or in both)

(A∪B) ∩C = {1,6,7,8,9} (intersection of two sets are the set of elements which are in both the sets)

Calculate P (D), i. e. power set of D

P (D) = {Ф,{1},{2},{1,2}} (Power set of any set is the collection of all the subsets of that set)

Is (A ∩ B) ⊆C? Why or why not?

A∩B={6,8}⊆{1, 4, 6, 7, 8, 9} = C

Hence, (A ∩ B) ⊆C

What is (B ∩ C) * {1,2}?

B∩C={6,7,8}

(B ∩ C) * {1,2}={6,7,8} * {1,2}

={ (6,1), (6,2), (7,1), (7,2), (8,1), (8,2) }