a) Prove that if f is a one-to-one function from A to B, then Sf is a one-to-one function from P(A) to P(B).
b) Prove that if f is an onto function from A to B, then Sf is an onto function from P(A) to P(B).
c) Prove that if f is an onto function from Ato B, then Sf-1 is a one-to-one function from P(B) to P(A).
d) Prove that if f is a one-to-one function from Ato B, then Sf-1 is an onto function from P(B) to P(A).
e) Use parts (a) through (d) to conclude that if f is a one-to-one correspondence from A to B, then Sf is a one-to-one correspondence from P(A) to P(B) and Sf-1 is a one-to-one correspondence from P(B) to P(A).
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