(1) If A is an even integer, and B is an even integer, prove (using a Direct Proof) that AB will result in an even integer as the answer. (20 pts.) (2) Prove the following statement by contradiction: There exist no INTEGER VALUES for A and B such that 9A+27B=1. (20 pts.) (3) For the following predicate statements, present a case that proves the statement is wrong. ( 10pts. each) (3.1) f(x)=(5x)/(10x) has a real answer for all values of x. (3.2) If A is an integer, and B is an integer, and A:=B, then (AB)>AAND(AB)>B. (4) Prove the following by induction (20 pts.) Series: (1/(1(1+1)),1/(2(2+1)),1/(3(3+1)),1/(4(4+1)), (c.) Sum of Series =n/(n+1) (5) Flashback to Logic Week: Convert the following statements into logic gate diagrams. (10 pts each.) (5.1) ((A xor B) or (C and A)) nor (B nand C) (5.2)(!(!A and B)) xnor (C or (B and !C))