Question
Download Solution PDFIf A is a finite set having n elements, then the number of relations which can be defined in A is
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFCalculation:
Set A has n elements.
Relation is simply A × A
So, we can select first element of ordered pair in n ways and second element in n ways.
So, clearly this set of ordered pairs contain n × n = n2 pairs.
Now, each of these n2 ordered pairs can be present in the relation or can't be. So, there are 2 possibilities for each of the n2 ordered pairs.
Thus, the total no. of relations = 2 × 2 × 2 × ......× (n2 times)
=
Hence, option (3) is correct.
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