Suppose that f is a function from the set A to the set B. Prove thata) if f is one-to-one, then Sf is a one-to-one function from p(A) to p(B).________________b) if f is onto function, then Sf is an onto function from p(A) to p(B).________________c) if f is onto function, then Sf?1 is a one-to-one function from p(B) to p(A).________________d) if f is one-to-one, then Sf is an onto function from p(B) to p(A).________________e) if f is a one-to-one correspondence, 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). [Hint: Use parts (a)-(d).]

8.1 Integration by Parts ❑ ❑ ❑ ❑ ❑ Deals with: ∫ xe dx, ∫ xcos(2 x)dx∫, l| | d∫ , e c(x)dx , etc… ❑ ❑ ❑ ❑ Consider: u(x) & v(x) 2❑different❑able functions: (❑*v)’=(u*v’)+(u❑*v) &(integrate ' with respect to x) uv=...