Help
Options
Didn't know it?
click below
click below
Knew it?
click below
click below
Don't Know
Remaining cards (0)
Know
retry
shuffle
restart
0:00
Embed Code - If you would like this activity on your web page, copy the script below and paste it into your web page.
Normal Size Small Size show me how
Normal Size Small Size show me how
Logic
Laws of Logic
| Question | Answer |
|---|---|
| MODUS PONENS (MP) -- direct reasoning applies to conditionals | If it rains, we will go to the movies. It rains. THEREFORE, we go to the movies. P-->Q and P, then Q |
| MODUS TOLLENS (MT) indirect reasoning applies to conditional) | If it rains, we will go to the movies. We don't go to the movies. THEREFORE, it didn't rain. P-->Q and ~Q, then ~P. (works because of the logical equivalence of the contrapositive) |
| LAW OF SYLLOGISM, a.k.a. "transitive property of conditionals" | P-->Q and Q-->R, then P-->R |
| Simplification - applies to AND statements only (CONJUNCTIONS) | If you know P˄Q, then you can say P by itself or Q by itself, they're both true!! |
| Equivalent Disjunctive (ED) -- magically turns a conditional statement into a disjunction OR | P --> Q ≡ ~P V Q |
| Disjunctive Syllogism - applies only to a DISJUNCTION | Either we go to the movies, or we go bowling. We don't go to the movies. Then we must have gone bowling! PVQ and ~P, then Q |
| Law of Contrapositive | P --> Q ≡ ~Q --> ~P |
| The inverse and the converse of a conditional statement are logically equivalent | Because they're contrapositives of each other! Inverse: ~P --> ~Q Converse: Q --> P |
| When is a disjunction false? Only one instance... | F V F = F |
| When is a conjunction true? Only one instance.... | T ˄ T = T |
| When is a conditional false? Only one instance, the broken promise... | T --> F = F |
| To negate a conditional, first rewrite it as a disjunction using th equivalent dusjunctive... | Then use Demorgan's Law: ~P--> Q) ≡ ~(~P V Q) ≡ P˄~Q |
| Other ways to say P --> Q "If P, then Q" | 1. P implies Q 2. Q if P 3. P only if Q |
| When is the biconditional true? Only two instances... | When the two statements are the SAME truth value, i.e. T <--> T, F <--> F |
| To translate the biconditional P <--> Q into words | P if and only if Q |
| DEMORGAN'S LAW - negates conjunctions and disjunctions | ~(PVQ)≡ ~P ˄ ~Q ~(P˄Q)≡ ~P V ~Q |
| The associative property only applies when all the conjunction/disjunction symbols are the same. Reassociate the parentheses | (A V B) V C ≡ A V (B V C) (A ˄ B) ˄ C ≡ A ˄ (B ˄ C) |
| Distributive property for conjuctions/disjunctions | A V (B ˄ C)≡ (AVB)˄(AVC) A ˄ (B V C)≡ (A˄B)V(A˄C) |
Created by:
kgkasper
Popular Math sets