THE GATEBOOK

Normalization Lectures

Two sets X and Y are said to have the same cardinality if and only if there is a one-to-one correspondence(i.e. Bijection) from X to Y. When A and B have the same cardinality, we write |X|=|Y|.

Let A and B be two sets such that . There is a one to one function from A to B.

Which of the following must be true for

S1: is onto function

S2: has an inverse

(A). Only S1

(B). Only S2

(C). Both S1 and S2

(D). None of the above

Above function is one-one but not onto.

https://en.wikipedia.org/wiki/Cardinality#:~:text=Two%20sets%20A%20and%20B,%E2%89%88%20B%20or%20A%20~%20B

https://youtu.be/k7qtU5HvGtM Watch this video start time 13:30 mint D is correct one

NOTE that if A or B is a finite set then Option C would be the answer.