Mathematical Reasoning: Writing and Proof (PreTeXt Edition)

Subsection Important Definitions

• Logically equivalent statements

• Converse of a conditional statement

• Contrapositive of a conditional statement

• Variable

• Universal set for a variable

• Constant

• Equal sets

• Predicate

• Open sentence

• Truth set of a predicate

• Universal quantifier

• Existential quantifier

• The Empty Set

• Counterexample 1 and Counterexample 2

• Perfect square

• Prime number

• Composite number

Subsection Important Theorems and Results

• Every theorem found in Theorem 2.12

• Theorem 2.24

Subsection Important Set Theory Notation