Question

Discrete math for Computer Science, Sets: Binary relations / Functions

Please show work

2. Let S = {0, 2, 4, 6), and T-1, 3, 5, 7). Determine whether each of the following sets of ordered pairs is a function from S to T. If so, is it injective, surjective, and bijective?

Answer 1

(a). It is a function but from S to S and not to S to T. Hence it is not a function from S to T.

(b). domain = { 6,2,0,4}

range = {3,1,3,5}

It is a function since every element in domain has exactly one yelement in the range.

It is an injective function since every element in S matches to some element(s) in T.

It is not subjective since 7 from T does not have any match in S.

(c). domain = {2,4,0,6}

range = {3,7,1,5}

It is a function since every element in domain has exactly one mathcig element in the range.

It is an injective function since every element in S mathes to some element in T.

It is subjective function since every element in T has some mathcing element in S.

It is bijectiver because it is both injective and subjective.