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Question
Let n(A) = m, and n(B) = n. Then the total number of non-empty relations that can be defined from A to B is ______.
Options
mn
nm – 1
mn – 1
2mn – 1
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Solution
Let n(A) = m, and n(B) = n. Then the total number of non-empty relations that can be defined from A to B is 2mn – 1.
Explanation:
Given that: n(A) = m and n(B) = n
∴ n(A × B) = n(A) . n(B) = mn
So, the total number of relations from A to B = 2mn – 1.
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