MASTERED - Discrete Math Basics to Memorize ;3

Proposition

• A sentence that is either T or F, but NOT both

• Called a “Statement”

• Denoted by Lowercase Letters

Logical Operator

An operation on one or more propositions that forms a new proposition

¬

Negation - The opposite truth value of a given proposition

Simple Proposition

A proposition that involves a single claim; cannot be broken down into any smaller components

Compound Proposition

A proposition that combines two or more simple propositions by applying a logical operator ursing logical connective words

Logical Connective Words

and, or, but, yet, if, only if, etc.

^

Conjunctive Statement - a logical statement that is true only if both propositions are true (AND)

∨

Disjunctive Statement - a logical statement that is true if at least one of the propositions is true. (OR)

→

Conditional Statement - ? (IF _ THEN_)

S.C.S - Converse

A logical statement formed by reversing the hypothesis and conclusion of a conditional statement. For example, if the original statement is "If P then Q," the converse is "If Q then P."

S.C.S - Inverse

A logical statement formed by negating both the hypothesis and conclusion of a conditional statement. For example, if the original statement is "If P then Q," the inverse is "If not P then not Q."

S.C.S - Contrapositive

A logical statement formed by negating the conclusion and the hypothesis of a conditional statement. For example, if the original statement is “If P then Q” then the contrapositive is “If not Q then not P”

Biconditional Statement

A logical statement that combines a conditional statement and its converse, expressed as “P if and only if Q”. It indicates that both conditions must either be true or false.

Precedence of Operators

1. Negation ¬

2. Conjunction ^

3. Disjunction v

4. Conditional →

5. IAOI <→