More Practice on Proofs

Select problems from the text (© McGraw Hill)

†The questions presented here have been adapted from Kenneth Rosen’s Discrete Mathematics and Its Applications, 8th Edition and Oscar Levin’s Discrete Mathematics:An Open Introduction.

Problem 1 ¶

Use a direct proof to show that the sum of two odd integers is even.

Problem 2 ¶

Show that if $n$ is an integer and $n^3 + 5$ is odd, then $n$ is even

Problem 3 ¶

Prove that if $n$ is an odd integer, then $n^3$ is an odd integer

Problem 4 ¶

Prove that if $x^3$ is irrational, then $x$ is irrational.

Problem 5 ¶

Prove that for all integers $a$ and $b$, if $a + b$ is odd, then $a$ is odd or $b$ is odd.