Logic Symbols Flashcards

Logic Symbols and Their Definitions

• Negation (~p): Represents the inverse of proposition p, indicating that p is not true.

• Conjunction (p ∧ q): A logical operator indicating that both propositions p and q must be true.

• Disjunction (p ∨ q): Refers to either proposition p or proposition q being true, allowing for both to be true simultaneously.

• Implication (p → q): Establishes a conditional relationship where the truth of p guarantees the truth of q, noted as "if p, then q."

• Biconditional (p ↔ q): Signifies that both propositions p and q are logically equivalent; they are either both true or both false.

• Logical Implication (p => q): Similar to implication, asserting that if proposition p holds true, then proposition q must also be true.

• Converse (q → p): The reversal of the original implication, where q implies p. Its truth value may differ from the original implication.

• Inverse (~p → ~q): Represents the negation of both propositions from the original implication, indicating that if p is false, then q must also be false.

• Contrapositive (~q → ~p): The negation and reversal of implication, where if q is false, p must also be false; inherently equivalent to the original implication.

• Tautology: A proposition that is always true regardless of the truth values of its constituent parts.

• Contradiction: A proposition that is always false, no matter the truth values assigned to its components.

• Universal Quantifier (∀x): Indicates that a statement applies to all elements x in a given set.

• Existential Quantifier (∃x): Indicates that there exists at least one element x in a set that satisfies a given condition.