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Consider two sets S1 and S2 of size 3 and 2 each.

(a) How many different functions are there from S1 to S2? From S2 to S1? (b) How many different relations are there from S1 to S2? From S2 to S2?

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  1. 27 December, 15:41
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    Explanation:

    function from S_1 to S_2 (functions have unique mapping

    each element in S_1 has 2 elements to map to in S_2 and there are 3 elements in S_1

    therefore number of functions = 2^3 = 8 (2 choices for each of 3 elements)

    a) relations between S_1 and S_2 are subset of S_1 x S_2

    there are 6 elements in S_1 x S_2 therefore relations would be 2^6 = 64

    (no of subsets of set of n elements = 2^n)

    b) By above explanation functions from S_2 to S_1 = 3^2 = 9

    and relation from S_2 to S_2 = 2^4 = 16
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