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Discrete Structures
Summary of Logical Equivalences
21
Computer Science
Undergraduate 2
01/28/2013
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Term
Commutative Laws
 Definition
p ^ q = q ^ p
Term
Identity Laws
 Definition
p ^ t = p
Term
Cummutative Laws
 Definition
p v q = p v q
Term
Associative Laws
 Definition
(p ^ q) ^ r = p ^ (q ^ r)
Term
Associative Laws
 Definition
(p v q) v r = p v (q v r)
Term
Distributive Laws
 Definition
p^(q v r) = (p^q) v (p ^ r)
Term
Distributive Laws
 Definition
p v (q ^ r) = (p v q) ^ (p v r)
Term
Identity Laws
 Definition
p v c = p
Term
Negation Laws
 Definition
p v ~p = t
Term
Negation Laws
 Definition
p ^ ~p = c
Term
Double Negative Law
 Definition
~(~p) = p
Term
Idempotent Laws
 Definition
p ^ p = p
Term
Idempotent laws
 Definition
p v p = p
Term
Universal Bound Laws
 Definition
p v t = t
Term
Universal Bound Laws
 Definition
p ^ c = c
Term
De Morgan's Laws
 Definition
~(p ^ q) = ~p v ~q
Term
De Morgan's Laws
 Definition
~(p v q) = ~p ^ ~q
Term
Absorption Laws
 Definition
p v (p ^ q) = p
Term
Absorption Laws
 Definition
p ^ (p v q) = p
Term
Negations of t and c
 Definition
~t = c
Term
Negations of t and c
 Definition
~c = t
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