Question 1194059: If S = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9} and A = {0, 2, 4, 6, 8}, B =
{1, 3, 5, 7, 9}, C = {2, 3, 4, 5}, and D = {1, 6, 7},
Draw the Venn diagram and list the elements of the sets
corresponding to the following events:
(a) A ∪ C;
(b) A ∩ B;
(c) C ;
(d) (C ∩ D) ∪ B;
(e) (S ∩ C) ;
(f) A ∩ C ∩ D.
Found 2 solutions by ikleyn, MathLover1:
Answer by ikleyn(52776)   (Show Source):
You can put this solution on YOUR website! .
(b) Set A consists of even numbers, while set B consists of odd numbers - - -
therefore, their intersection is empty set.
A ∩ B = empty set.
(c) C is just given in the post; therefore, there is no need to ask again about C.
(e) (S ∩ C) is the same as C: S ∩ C = C, because S plays a role of the universal set in this problem.
Answer by MathLover1(20849)  (Show Source):
You can put this solution on YOUR website!
(a) A ∪ C={0, 2, 4, 6, 8} ∪ {2, 3, 4, 5}={0, 2,3, 4, 5,6, 8}
(b) A ∩ B={0, 2, 4, 6, 8} ∩ {1, 3, 5, 7, 9}= { } (empty set)
(c) C ; as given: C = {2, 3, 4, 5}
(d) (C ∩ D) ∪ B= ({2, 3, 4, 5} ∩ {1, 6, 7}) ∪ {1, 3, 5, 7, 9}={ }∪ {1, 3, 5, 7, 9}= {1, 3, 5, 7, 9}
(e) (S ∩ C)={0, 1, 2, 3, 4, 5, 6, 7, 8, 9} ∩ {2, 3, 4, 5}={2, 3, 4, 5}
(f) A ∩ C ∩ D={0, 2, 4, 6, 8} ∩ {2, 3, 4, 5} ∩ {1, 6, 7}={ } (empty set)
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