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Discrete math proofs

(See attached file for full problem description with proper symbols and equations)

1)Prove that for any non-empty sets
A x (B-C) = (AxB)-(AxC)

2) Let a,b be integers and m a positive integer. Prove that:
ab = [(a mod m ) * (b mod m) mod m ]

3)Prove or disprove (a mod m) + (b mod m) = (a+b) mod m for all integers a and b whenever m is a positive integer.

4) prove that
floor(n/2) * ceiling(n/2) = floor (n2/4)

5) For any integer n show that 7n+1 and 15n+2 are relatively prime

6) By induction show that
1*2*3 + 2*3*4 +...n(n+1)(n+2) = n(n+1)(n+2)(n+3)/4


Solution Summary

There are a series of discrete math proofs here regarding sets, relative primes, floor and ceiling, and modulo arithmetic.