• Shuffle
    Toggle On
    Toggle Off
  • Alphabetize
    Toggle On
    Toggle Off
  • Front First
    Toggle On
    Toggle Off
  • Both Sides
    Toggle On
    Toggle Off
  • Read
    Toggle On
    Toggle Off
Reading...
Front

Card Range To Study

through

image

Play button

image

Play button

image

Progress

1/26

Click to flip

Use LEFT and RIGHT arrow keys to navigate between flashcards;

Use UP and DOWN arrow keys to flip the card;

H to show hint;

A reads text to speech;

26 Cards in this Set

  • Front
  • Back

tautology

statements that are always true for every line of the truth table

contradiction

a statement that is false for every line of the truth table

contingent

a statement with mixed truth values

logically equivalent

they have the same truth values for every line of the truth table

logically contradictory

they have opposite truth values on every line of the truth table

logically inconsistent

there is no row of the truth table in which both statements are true

modus ponens

p--> q


p, so q

modus tolens

p--> q


~q, so ~ p

disjunctive syllogism

p v q


~p, so q or ~q, so p

simplication

p*q


so p, or so q

conjunction

if p and if q, then p*q

hypothetical syllogism

p-->q, q-->r, so p-->r

addition

if p is true, then p v (any variable) is true

constructive dilemma

pvq


p--> r


q-->s so, rvs

double negation

p:: ~~p

commutation

(pvq) :: (qvp)


(p*q) ::(q*p)

association

pv (qvr) :: (pvq) vr




p*(q*r) :: (p*q)*r

DeMorgan's Law

~(pvq) :: (~pv~q)


~(p*q) :: (~p*~q)

contraposition

p-->q :: ~q-->~p

distribution

(p*[qvr]) :: (p*q) v (p*r)


(pv[q*r]) :: (pvq) * (pvr)

exportation

(p*q)-->r :: p--> (q-->r)

redundancy

p*p :: p


pvp :: p

material equivalence

p<-->q :: (p*q) v (~p*~q) (either they are both true, or neither are true)


p<-->q :: (p-->q) * (q-->p)



material implication

(p-->q) :: ~pvq (either p is not true, or q istrue

conditional proof

conclusion must be a conditional, biconditional, or a disjunct that can be made into a conditional


(assume that the antecedent of the conclusion is true, and solve)

indirect proof

assume conclusion is false, and find the contradiction in the premises (if there is a contradiction, then it is wrong to assume the conclusion is false)