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
Discrete Structures
Logical Connectives
| Question | Answer |
|---|---|
| ER: Commutative (Comm) | Switches Expressions - Ex: R v S = S v R |
| ER: Associative (Ass) | Switches parentheses - Ex: (R v S) v Q = R v (S v Q) |
| ER: De Morgan’s Laws | With negation, turns expressions & logical connective the opp. - Ex: (R v S)’ = R’ ^ S’ - (R ^ S)’ = R’ v S’ |
| ER: Implication (Imp): | Shortens abbs. | P → C - Ex: R → S = R’ v S - R’ → S = R v S - The reason why we prefer this is b/c R v S doesn’t tell us if 1 expressions is (-) |
| ER: Double Negation (Dn) | Expressions = DnExpressions - Ex: R = (R’)’ |
| ER: Equivalence (Equ) | Shortens abb. - Ex: P ←→ Q = (P → Q) ^ (Q → P) |
| IR: Modus Ponens (Mp) | Proves the antecedent/Conclusion if Pn is true - Ex: R, R → S = S - If R is true then you make a truth table & cross out the possibilities and you’re derived/left with S |
| IR: Modus Tollens (Mt) | Disapproves consequent/Pn if Conclusion is false - Ex: R → S, S’ = R' - If S’ is true, then S is false & R → S is true. You are only left with 1 possibility which makes R false/R’ |
| IR: - Conjunction (Con) | If indiv. expressions are true then Conclusion true since ^ - Ex: R, S = R ^ S |
| IR: Simplification (Sim) | If combined wff is true then indiv expressions are true - Ex: R ^ S = R, S |
| IR: Addition (add) (ON) | Conclusion can be true from 1 expression b/c it works no matter what value you put the extra expression with - Ex: R = R v S |
| Disjunction Syllogism (Ds) | If P’ is true then P is false & Q is true to make P v Q true - P v Q, P' = Q |
| Contraposition (Cont) | P -> Q =Q' -> P' |
| P v Q =? | P' -> Q Q' -> P |
Created by:
Whateverisfree