10 Replacement Rules

Duplication

p : : p v p

p : : p *p

Permits inverting of conjuncts, disjuncts

p v q : : q v p

p * q : : q * p

Commutation

p v q : : q v p

p * q : : q * p

Permits regrouping of iterated disjuntions or conjuncts

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

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

Association

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

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

Permits inverting of conditionals, with appropriate negation changes

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

Contraposition

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

Permits distribution of negation across disjunctions and conjunctions used extensively

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

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

De Morgan's

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

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

Permits introduction and elimination of triple bar

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

Biconditional Exchange

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

Permits exchange of conditional and disjuntion

p [hs] q : : ~p v q

Conditional Exchange

p [hs] q : : ~p v q

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)

Distribution

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