Discrete Math Let A be a set and PA be the power set of A Tr

Discrete Math:

Let A be a set and P(A) be the power set of A. True or false with explanation

a. There is an injection from A to P(A).

b. There is a surjection from A to P(A).

Solution

Cardinality of power set P(A) is more than set A

a. Injection from A to P(A) is true as an element P(A) is connected with atmost one element of A.

b.

Surjection from A to P(A) is false at there is elements in P(A) which are not connected with A.