1. Prove or disprove each of the following statements. (a) For all sets A, B and C, if A- (BUC) = then A-B=0 or A-C=0. (b) For all sets A, B and C. if A- (BOC) = then A-B=0 and A-C=0. (c) For all sets A, B and C, if A x B C AXC then BCC. (d) For all sets A, B and C, if Ax BCA x C and Athen BCC. 2. (a) Prove that for all integers n. n +n is even. (b) Prove by induction on n that (-1)"-12= (-1)-1(+) for all integers n 1. i=1 (c) Prove by induction on n that 5n +n is divisible by 6 for all integers n 1. 3. Prove the following statements by induction on n. (a) (1+1)">1+ for all integers n 1. (b) > for all integers n 2.