MMW TERMS#1

Proposition

a declarative sentence that can be objectively identified as either true or false, but not both.

Truth table

a diagram in table form that is used to show all its possible truth values.

Quantified statements

involve terms such as all, each, every, no, none, some, there exists, and at least one.

Universal quantifiers

use the words: all, each, every, no, and none

Existential quantifiers

use the words: some, there exists, and at least one

Negation

the proposition which is false when p is true; and true when p is false.

Simple proposition

a proposition with only one subject and only one predicate and cannot be deduced to simpler propositions. It conveys a single idea.

Compound proposition

a proposition formed by joining two or more simple propositions with a connective. It conveys two or more ideas.

Conjunction

denoted by p ∧ q, is true only when both p and q are true, and is false otherwise.

Disjunction

denoted by p ∨ q, is false only when both p and q are false, and is true otherwise.

Exclusive or

denoted by “p ⊻q” or “p ⊕ q”, is the proposition that is true when exactly one of p and q is true, and is false otherwise.

Conditional

denoted by p → q, is false when p is true and q is false, and true otherwise. p is called the hypothesis (or antecedent or premise) and q is called the conclusion (or consequence).

Biconditional

denoted by p ↔ q, true only if p and q have the same truth values, and is false otherwise.

Tautology

compound proposition that is always true

Contradiction

compound proposition that is always false

Contingency

compound proposition that is neither a tautology nor a contradiction