Symbolic Logic Test Questions with Correct Answers Latest Update 2025

Symbolic Logic Test Questions with Correct Answers Latest Update 2025 ¬ - Answers NOT (__negation__The statement ¬A is true if and only if A is false. A slash placed through another operator is the same as "¬" placed in front. ) ∧ - Answers AND (__conjunction__The ampersand ( & ) or dot ( · ) are also often used.) ∨ - Answers OR (__disjunction__ This is the inclusive disjunction, equivalent to and/or in English.) ⊕ - Answers exclusive disjunction (XOR) (⊕ means that only one of the connected propositions is true, equivalent to either...or. Sometimes ⊻ is used.) | - Answers alternative denial (NAND) (Means "not both". Sometimes written as ↑) ↓ - Answers joint denial (NOR) (Means "neither/nor".) → - Answers if/then (__conditional__Many logicians use the symbol ⊃ instead. This is also known as material implication.) ↔ - Answers biconditional (iff) (Means "if and only if" ≡ is sometimes used, but this site reserves that symbol for equivalence.) ∀ - Answers universal quantifier (Means "for all", so ∀xPx means that Px is true for every x.) ∃ - Answers existential quantifier (Means "there exists", so ∃xPx means that Px is true for at least one x.) ⊨ - Answers implication (α ⊨ β means that β follows from α) ≡ - Answers equivalence (Also ⇔. Equivalence is two-way implication, so α ≡ β means α implies β and β implies α.) ⊢ - Answers provability (Shows provable inference. α is provable β means that from α we can prove that β.) ∴ - Answers therefore (Used to signify the conclusion of an argument. Usually taken to mean implication, but often used to present arguments in which the premises do not deductively imply the conclusion.) ⊩ - Answers forces (A relationship between possible worlds and sentences in modal logic.) ⊤ - Answers tautology (May be used to replace any tautologous (always true) formula.) ⊥ - Answers contradiction (May be used to replace any contradictory (always false) formula. Sometimes "F" is used. ( ) - Answers parentheses (Used to group expressions to show precedence of operations. Squa