Logic Symbols Flashcards

Questions and Answers

What is the negation of p?

p ∨ q

p ∧ q

p → q

~p (correct)

What is the logical conjunction of p and q?

p ∧ q

What does p ∨ q represent?

Disjunction: p OR q

What does p → q mean?

Implication: IF p THEN q Signup and view all the answers

What is the biconditional of p and q?

p ↔ q Signup and view all the answers

What does p => q signify?

Logical implication: p IMPLIES q Signup and view all the answers

What is the converse of the implication p → q?

q → p Signup and view all the answers

What does ~p → ~q signify?

Inverse of p → q Signup and view all the answers

What is the contrapositive of p → q?

~q → ~p Signup and view all the answers

What is a Tautology?

Always true Signup and view all the answers

What is a Contradiction?

Always false Signup and view all the answers

What does ∀x represent?

Universal Quantifier: For ALL x Signup and view all the answers

What does ∃x mean?

Existential quantifier: For SOME x Signup and view all the answers

Study Notes

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.

Description

Test your knowledge of basic logic symbols with these flashcards. Each card presents a symbol along with its definition, helping you understand the foundational concepts of logic. Perfect for students and anyone interested in improving their logical reasoning skills.