Show that if n is an integer and n³+5 is odd, then n is even using
(a) A proof by contraposition
(b) A proof by contradiction

Prove the proposition P(0), where P(n) is the proposition “If n is a positive integer greater than 1, then n²n”. What kind of proof did you use?

Let P(n) be the proposition “If a and b are positive real numbers, then (a+b)ⁿ≥aⁿ+bⁿ”, prove that P(1) is true.

Prove that if n is a positive integer, then n is odd if and only if 5n+6 is odd.

Prove that n²+1≥2ⁿ when n is a positive integer with 1≥n≥4.

Use proof by cases to prove that if x and y are real numbers then max?(x,y)+min?(x,y)=x+y.

Prove using (WLOG) that for every real numbers x and y,

Prove the proposition P(n) that the sum of the first n positive integers is



Prove the following proposition (for n≥0 ):