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Question
A, B and C are subsets of Universal Set U. If A = {2, 4, 6, 8, 12, 20} B = {3, 6, 9, 12, 15}, C = {5, 10, 15, 20} and U is the set of all whole numbers, draw a Venn diagram showing the relation of U, A, B and C.
Solution
A = {2, 4, 6, 8, 12, 20}
B = {3, 6, 9, 12, 15}
C = {5, 10, 15, 20}
Here, U is a universal set
Therefore,
⇒ A ∩ B = {2, 4, 6, 8, 12, 20} ∩ {3, 6, 9, 12, 15}
= {6, 12}
⇒ B ∩ C = {3, 6, 9, 12, 15} ∩ {5, 10, 15, 20}
= {15}
⇒ A ∩ C = {2, 4, 6, 8, 12, 20} ∩ {5, 10, 15, 20}
= {20}
⇒ A ∩ B ∩ C = {2, 4, 6, 8, 12, 20} ∩ {3, 6, 9, 12, 15} ∩ {5, 10, 15, 20}
= { }
Hence, the Venn diagram showing relation of given sets is:
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