PS-02-Solution-Proofs.pdf - Discrete Structures Assignment...

Discrete Structures
Assignment 02
Propositional Logic, Proofs Techniques and Time Complexity
Date of Submission: Thursday, 04-NOV-2017, 11.59PM
1. Prove any 4 of the following claims: (20 Points)
(a) If 7 n + 4 is even then n is even.
(b) If n is even then 7 n + 4 is even.
(c) If mn is even then m is even or n is even.
(d) If r is rational then r 3 + r + 1 6

2. Prove the following Claims: (10 Points)
(a) If x and y are natural numbers and gcd ( x, y ) = 1 (they have no common factors greater than 1),
then log
x
y (log of y base x) is irrational.