set theory and algebra

Question

Answer 1

I feel
           A) g should be should be one-to-one.
           B) g neednot be onto.

Comments

can you pls explain or give any reference??

Answer 2

for these type of question try to create 1 counter example if u succeed then then given statement is not correct else correct

 

for these two question it is not possible to disprove using counter example implies that both are correct