Appendix 1: Proofs in Mathematics — Formula Sheet

Proof = chain of deductive statements

Two ways of proving a proposition: directly and indirectly

x^2 - 5x + 6 = x^2 - 3x - 2x + 6 = x(x - 3) - 2(x - 3) = (x - 3)(x - 2)

f(x_1) = f(x_2) \Rightarrow x_1 = x_2

~q \Rightarrow ~p

A^{-1} = \frac{adj A}{|A|}

f(x) = 2x + 5

\u03c6(x) = |x|

Example 1 uses factorisation to show x^2 - 5x + 6 = 0 implies x = 3 or x = 2.