Assignment:
Q1)Prove that for any non-empty sets
A x (B-C) = (AxB)-(AxC)
Q2) Let a,b be integers and m a positive integer. Prove that:
ab = [(a mod m ) * (b mod m) mod m ]
Q3) 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.
Q4) Prove that
floor(n/2) * ceiling(n/2) = floor (n2/4)
Q5) For any integer n show that 7n+1 and 15n+2 are relatively prime
Q6) By induction show that
1*2*3 + 2*3*4 +…n(n+1)(n+2) = n(n+1)(n+2)(n+3)/4
Provide complete and step by step solution for the question and show calculations and use formulas.