Hw3 1. Prove by induction that XXXXXXXXXX + −+ nbydivisibleisnn 2. Compute XXXXXXXXXXmod 13 3. Solve the following puzzle : ???? ?ℎ? ???????? ??????? ? ????????? ?ℎ? ?????????: ? = 2 ??? 3 ? = 4 ???...

Hw3 1. Prove by induction that 1723 112 + −+ nbydivisibleisnn 2. Compute 2017 2017 mod 13 3. Solve the following puzzle : ???? ?ℎ? ???????? ??????? ? ????????? ?ℎ? ?????????: ? = 2 ??? 3 ? = 4 ??? 5 ? = 6 ??? 7 4. Prove or disprove : For all sets A and B, ( )A A B A= 5. Suppose E is an equation of set algebra. The dual E* of E is the equation obtained by replacing each occurrence of Uand, in E by andU respectively. Find the dual equation for the following : E Dual of E , E* 1 '')'( BABA  = 2 )()()( CABACBA  = 3 UAA =' 4 ABAA =)(  5 AUA =