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Question
If R is a relation on a finite set having n elements, then the number of relations on A is
Options
(a) 2n
(b) \[2^{n^2}\]
(c) n2
(d) nn
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Solution
(b) \[2^{n^2}\]
Given : A finite set with n elements
Its Cartesian product with itself will have n2 elements.
∴ Number of relations on A = \[2^{n^2}\]
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