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Question
Using the Venn diagram, examine the logical equivalence of the following statements:
(a) Some politicians are actors.
(b) There are politicians who are actors.
(c) There are politicians who are not actors.
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Solution
Let the universal set be U.
U : The set of all human beings.
Let P: The set of all politicians.
A: The set of all actors.
Now, the Venn diagrams for statements (a). (b) and (c) are as follows:
(a)
(b)
(c)
By Venn diagrams, we observe that the truth set of statements (a) and (b) are equal. Hence statements (a) and (b) are logically equivalent.
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