Question

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?

Answer 1

Answer:

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