# 10 Replacement Rules

- StudyBlue
- Wisconsin
- University of Wisconsin - Milwaukee
- Philosophy
- Philosophy 211
- Tierney
- 10 Replacement Rules

**Created:**2009-03-26

**Last Modified:**2011-06-24

#### Related Textbooks:

Understanding Symbolic Logic (5th Edition)**Double Negation**

Permits introduction and elimination of pairs of tildes

p : : ~~p

**Double Negation**

p : : ~~p

**Duplication**

Permits introduction and elimination of redundant disjuncts and conjuncts

p : : p v p

p : : p * p

**Duplication**

p : : p v p

p : : p *p

**Commutation**

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

**Association**

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

**Contraposition**

Permits inverting of conditionals, with appropriate negation changes

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

**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

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)

**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

**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)

**Distribution**

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

**Exportation**

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