Question

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

Answer 1

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)}