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?

Answered

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