Use the rules of inference and the laws of logic to prove the logical equivalence of the two statements. If the argument
Posted: Fri Jul 01, 2022 5:46 am
Use the rules of inference and the laws of logic to prove thelogical equivalence of the two statements. If the argument is notvalid, give truth values that demonstrate that it is an invalidargument. USE THE FORMULA BELOW TO PROVE, DO NOT USE THETRUTH TABLE.
2. → b - d p/r r → U nvb ::
Rule of inference P p-q Aq 9 -Q p-q -p pvq PAq AP P q APAq p-q Apr pvq -P Aq pvq -pvr Aqvr Name Modus ponens Modus tollens Addition Simplification Conjunction Hypothetical syllogism Disjunctive syllogism Resolution
Table 1.5.1: Laws of propositional logic. Idempotent laws: Associative laws: Commutative laws: Distributive laws: Identity laws: Domination laws: Double negation law: Complement laws: pvp = p (pvq) vr=pv (qvr) pvq=qvp p ^ q = q^р pv (q^r) = (pvq) ^ (pvr) p^(qvr) = (p^q) v (par) рлт=р pvT=T pvF=p P&F=F ¯¯p = p р^-p=F -T=F р^р = р (рла)лг=рл (q^г) De Morgan's laws: -(pvq)=-^- Absorption laws: pv (p^q) = p Conditional identities: p q = pv q pv-p=T ¬F=T -(q) = q p^ (pvq) = p pq=(pq) ^ (q→p)
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Rule of inference P p-q Aq 9 -Q p-q -p pvq PAq AP P q APAq p-q Apr pvq -P Aq pvq -pvr Aqvr Name Modus ponens Modus tollens Addition Simplification Conjunction Hypothetical syllogism Disjunctive syllogism Resolution
Table 1.5.1: Laws of propositional logic. Idempotent laws: Associative laws: Commutative laws: Distributive laws: Identity laws: Domination laws: Double negation law: Complement laws: pvp = p (pvq) vr=pv (qvr) pvq=qvp p ^ q = q^р pv (q^r) = (pvq) ^ (pvr) p^(qvr) = (p^q) v (par) рлт=р pvT=T pvF=p P&F=F ¯¯p = p р^-p=F -T=F р^р = р (рла)лг=рл (q^г) De Morgan's laws: -(pvq)=-^- Absorption laws: pv (p^q) = p Conditional identities: p q = pv q pv-p=T ¬F=T -(q) = q p^ (pvq) = p pq=(pq) ^ (q→p)