• Most mathematical theorems are conditional statements: if p (hypothesis) then q (conclusion). There are three common techniques of proof; (i) Explain about direct proof (of if p then q). For an example, prove directly that "if n is an even integer, then n^2 is even." (ii) Explain about proof by contraposition. Prove by contraposition that "if m^2 is even, then m is even." (iii) Explain about proof by contradiction. Prove by contradiction that "if x is real and x^2 = 3, then x is irrational".