Table of Logical Equivalences

Table of Logical EquivalencesCommutativep q q pp q q pAssociative(p q) r p (q r)(p q) r p (q r)Distributivep (q r) (p q) (p r)p (q r) (p q) (p r)Identityp T pp F pNegationp p Tp p FDouble Negative ( p) pIdempotentp p pp p pUniversal Boundp T Tp F FDe Morgan s (p q) ( p) ( q) (p q) ( p) ( q)Absorptionp (p q) pp (p q) pConditional(p= q) ( p q) (p= q) (p q)Rules of InferenceModus Ponensp= qModus Tollensp= qp q q pEliminationp qTransitivityp= q qq= r p p= rGeneralizationp= p qSpecializationp q= pq= p qp q= qConjunctionpContradiction Rule p= Fq p p q 2011 for This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike Unported License.

Jul 20, 2011 · Conditional (p =)q) ()(˘p_q) ˘(p =)q) ()(p^˘q) Rules of Inference Modus Ponens p =)q Modus Tollens p =)q p ˘q) q )˘p Elimination p_q Transitivity p =)q ˘q q =)r) p ) p =)r Generalization p =)p_q Specialization p^q =)p q =)p_q p^q =)q Conjunction p Contradiction Rule ˘p =)F q ) p) p^q « 2011 B.E.Shapiro forintegral-table.com.

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