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.