Laws of logical connectives Laws of logical connectives

1. Commutative laws
1.

p∨q=q∨p $p vv q = q vv p$
2.

p∧q=q∧p $p ^^ q = q ^^ p$

2. Associative laws
1.

(p∨q)∨r=p∨(q∨r) $(p vv q) vv r = p vv (q vv r)$
2.

(p∧q)∧r=p∧(q∧r) $(p ^^ q) ^^ r = p ^^ (q ^^ r)$

3. De-Morgan's laws
1.

~(p∨q)=~p∧~q $~(p vv q) = ~ p ^^ ~ q$
2.

~(p∧q)=~p∨~q $~(p ^^ q) = ~ p vv ~ q$

4. Distributive laws
1.

p∧(q∨r)=(p∧q)∨(p∧r) $p ^^ (q vv r) = (p ^^ q) vv (p ^^ r)$
2.

p∨(q∧r)=(p∨q)∧(p∨r) $p vv (q ^^ r) = (p vv q) ^^ (p vv r)$

5. Negation law
1.

~(~p)=p $~(~ p) = p$

6. Absorption laws
1.

p∧(p∨q)=p $p ^^ (p vv q) = p$
2.

p∨(p∧q)=p $p vv (p ^^ q) = p$

This material is intended as a summary. Use your textbook for detail explanation.
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