Let $n (A) = m, n (B) = n$ , then the total number of non-empty relations that can be defined from $A$ to $B$ is

2^{m n}

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(m n)^{2} - 1

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(m n - 1)^{2}

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2^{m n} - 1

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Solution

The correct option is D $2^{m n} - 1$
Total relations $= 2^{m n}$
$∴$ Non- empty relations $= 2^{m n} - 1$

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n (A) = m, n (B) = n

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n (A) = m

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If n(A) = m and n(B)= n, find the total number of non-empty relations that can be defined from A to B.

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
(a) mⁿ
(b) n^m − 1
(c) mn − 1
(d) 2^mn − 1

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