Q. 12

# Mark the correct alternative in the following:

If *R* is a relation from a finite set *A* having *m* elements to a finite set *B* having *n* elements, then the number of relations from *A* to *B* is

A. 2^{mn}

B. 2^{mn}− 1

C. 2*mn*

D. *m*^{n}

^{mn}

^{mn}

^{n}

Answer :

Since we know that a relation from A to B consists of mn ordered pairs if they contain m and n elements respectively..

Each subset of those mn pairs will be a relation..so, each pair has two choices, either to be in that particular relation or not.

So, we have a tptal of 2^{mn} relations.

Therefore, option A is correct.

Rate this question :

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(i) A = (–2, 3)

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(v) E = [–10, 0)

(vi) F = (0, 5]

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If *R* is a relation from a finite set *A* having *m* elements to a finite set *B* having *n* elements, then the number of relations from *A* to *B* is

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