Discrete math

Math 42 Homework 3 . Give a direct proof of the following theorem. "Ifo and b are odd integers, then ab is an odd integer\" . Give a direct proof of the following theorem. If n. is an integer divisible by 3 and b is an integer divisible by 2. then ob is an integer divisible by (i " . Give a proof by contraposition of the following theorem. \"If-n is an integer and n3 + 5 is odd, then :1 is even" . Use a proof by contradiction to prove that the sum of an irrational number and a rational number is irrational. . Prove that \\/ is irrational