10 Replacement Rules - Philosophy 211 with Tierney at University of Wisconsin - Milwaukee

Chris M.

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Related Textbooks:

Understanding Symbolic Logic (5th Edition)

Double Negation

Permits introduction and elimination of pairs of tildes

p : : ~~p

Permits introduction and elimination of pairs of tildes

Double Negation

p : : ~~p

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Duplication

Permits introduction and elimination of redundant disjuncts and conjuncts

p : : p v p

p : : p * p

Permits introduction and elimination of redundant disjuncts and conjuncts

Duplication

p : : p v p

p : : p *p

Commutation

Permits inverting of conjuncts, disjuncts

p v q : : q v p

p * q : : q * p

Permits inverting of conjunctions, disjunctions

Commutation

p v q : : q v p

p * q : : q * p

Association

Permits regrouping of iterated disjuntions or conjuncts

p v (q v r) : : (p v q) v r

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

Permits regrouping of iterated disjunctions or conjuntions

Association

p v (q v r) : : (p v q) v r

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

Contraposition

Permits inverting of conditionals, with appropriate negation changes

p [horseshoe] q : : ~q [horseshoe] ~p

Permits inverting of conditionals, with appropriate negation changes

Contraposition

p [horseshoe] q : : ~q [horseshoe] ~p

De Morgan's

Permits distribution of negation across disjunctions and conjunctions used extensively

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

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

Peion of negation across disjuntions and conjunctions used extensively

De Morgan's

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

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

Biconditional Exchange

Permits introduction and elimination of triple bar

p [tb] q : : (p [hs] q) * (q [hs] p)

Permits introduction and elimination of triple bar

Biconditional Exchange

p [tb] q : : (p [hs] q) * (q [hs] p)

Conditional Exchange

Permits exchange of conditional and disjuntion

p [hs] q : : ~p v q

Permits exchange of conditional an disjunction

Conditional Exchange

p [hs] q : : ~p v q

Distribution

Permits changing of major operator from* tov and vice versa

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

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

Permits changing of major operator from * to v an dvice versa

Distribution

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

Exportation

p [hs] (q [hs] r) : : (p * q) [hs] r

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