Elementary Logic

Mathematical Induction

The study of processes used in mathematical induction.

Inductive Reasoning

Reasoning based on observations and conclusions drawn from them.

Deductive Reasoning

Reasoning based on facts and rules to draw conclusions.

Propositional Logic

The study of logical relationships between propositions.

Proposition

A statement that can be either true or false, but not both.

Logical Operators

Symbols used in propositional logic to combine or modify propositions.

Negation (¬)

Denotes the logical opposite of a proposition.

Conjunction (∧)

Logical operator representing "and" between propositions.

Disjunction (∨)

Logical operator representing "or" between propositions.

Inclusive Disjunction

Disjunction where both propositions being joined are false.

Exclusive Disjunction

Disjunction where both propositions being joined have the same truth value.

Implication/Conditional (→)

Logical operator representing "if...then" between propositions.

Biconditional (↔)

Logical operator representing "if and only if" between propositions.

Tautology

A statement that is always true, regardless of the truth values of its components.

Contradiction

A statement that is always false, regardless of the truth values of its components.

Logical Equivalence

Two statements that always have the same truth value.

Converse

The switching of hypothesis and conclusion in a conditional statement.

Inverse

The negation of both the hypothesis and conclusion in a conditional statement.

Contrapositive

The combination of switching hypothesis and conclusion and negating both in a conditional statement.