Discrete StructuresAssignment 02Propositional Logic, Proofs Techniques and Time ComplexityDate of Submission: Thursday, 04-NOV-2017, 11.59PM1. Prove any 4 of the following claims:(20 Points)(a) If 7n+ 4 is even thennis even.(b) Ifnis even then 7n+ 4 is even.(c) Ifmnis even thenmis even ornis even.(d) Ifris rational thenr3+r+ 16
2. Prove the following Claims:(10 Points)(a) Ifxandyare natural numbers andgcd(x, y) = 1 (they have no common factors greater than 1),then logxy(log of y base x) is irrational.