Propositional Logic Flashcards
what does this symbol mean? ^
and - conjunction
what does this symbol mean? V
or - disjunction
what does this symbol mean? ⊃
if, then, conditional
what does this symbol mean? ≡
iff, biconditional
what does this symbol mean? ˜
not, negation
what is the truth table for ^
^ T T | T T F | F F T | F F F | F
what is the truth table for V
V T T | T T F | T F T | T F F | F
what is the truth table for ⊃
⊃ T T | T T F | F F T | T F F | T
what is the truth table for ≡
≡ T T | T T F | F F T | F F F | T
what is the truth table for ˜
˜
T | F
F | T
what is a ‘main operator’?
whichever symbol has the widest scope over the logical formula
what is a tautology? what has to be the case on a truth table for a formula to be considered one?
a formula that can never be false
- results in all T’s
what is a contraction? what has to be the case on a truth table for a formula to be considered one?
a formula that can never be true.
- results in all F’s
how do you check for validity?
if the premises are true then the conclusion must be true. check for invalidity - is there an instance where premises are true but conclusion false?
what do you call two logical equivolents presented as a formula ?
a tautology
