Question

If for sets A and B there exists an injective function but not bijective function from A to B then?

(a) Cardinality of A is  strictly greater than B

(b) Cardinality of B is  strictly greater than A

(c) Cardinality of B is equal to A

(d) None of the mentioned

The question was posed to me by my school teacher while I was bunking the class.

Asked question is from Cardinality of Sets topic in portion Basic Structures: Sets, Functions, Sequences, Sums and Matrices of Discrete Mathematics

Answer 1

The correct choice is (b) Cardinality of B is  strictly greater than A

The best I can explain: If there doesnot exist a bijective function from A to B that means there are some elements in B whose preimage is not in A, thus cardinality of B is strictly greater than A.