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)}
