Prove that these four statements are equivalent: i)n^2 is odd, (ii) 1 - n is even, (iii) n^3 is odd , (iv) n^2 +1 is even

Prove that these four statements are equivalent: i) n^2 is odd, (ii) 1 - n is even, (iii) n^3 is odd , (iv) n^2 +1 is even

Methods of proof

Prove that the square of an even number is an even number using: a) a direct proof b) an indirect proof c) proof by contradiction

Methods of proof

Prove that if n is a positive integer, then n is even if and only if 7n+4 is even

Methods of proof

Show that these three statements are equivalent where a and be are real numbers: i) a is less than b II) the average of a and b is greater than a III) the average of a and b is less than b

Recursive Definitions

A better understanding of how these problems are done.