• Also known as Proposition
  • Can be presented with variables like p, q, r & s which return either True or False etc. Statements expressed in variables are called Statement Form
  • 3 important types are Conditional Statement, Universal Statement, & Existential Statement. We can form complex statements that are made of more than one type

Keep It Atomic

This makes the cognitive load low, easier to build on top of the statement, especially for Mathematical Proof that is complicated


  1. Predicate without value substituted to its Predicate Variable isn’t mathematical statement, unless it is Logical Equivalence equation that involves predicate. For example
  2. Not in a question form
  3. Either True or False, but not both at the same time

Compound Statement


When the statement has Conditional Statement, convert it using Implication Law to make it much less confusing

Special Mathematical Statements

Axioms (公理)

Theorem (定理)

Lemma (引理)

Corollary (推论)

  • A result that is a simple deduction from a Theorem (定理)
  • For example, we proof that the product of any two odd numbers is always odd. The corollary is the product of two sonsecutive odd numbers is always odd

Conjecture (猜测)



Contradiction c