TABLE 6 Logical Equivalences.
Equivalence
Name
p AT=.p
Identity laws
p VF=.p
Domination laws
p vT=.T
pAF=.F
pvp=.p
Idempotent laws
p Ap=.p
-.(-.p) =. p
Double negati on law
p vq=.q Vp
Commutative laws
p Aq=.q Ap
(p
q) V r
V
(p A q) A r
p V (q A r)
p A (q V r)
== (p
== (p
==
==
-.(p
A
q)
-.(p
v
q)
P
(p A q)
V
== p V
== p A
-'P
v
Associative laws
(q V r)
(q A r)
V
q) A (p V r)
A
q) V (p A r)
Distributive laws
De Morgan's laws
-.q
-'P A -'q
==
Absorption laws
p
p A(P Vq)==p
p v -'P
p A -.p
== T
== F
Negation laws
---TABLE 7 Logical Equivalences
Involving Conditional Statements.
p
~
P
~
== -'P V q
q == -.q ~ -'P
q
P V q == -'P
P
A
q
==
~
q
-'(p ~ -.q)
-'(p ~ q)
== P A
(p ~ q)
A
(p ~ r)
(p ~ r)
A
(q ~ r)
-.q
(p ~ q) v (p ~ r)
(p ~ r)
V (q
~ r)
TA B LE 8 Logical
Equivalences Involving
Biconditionals.
P
B
P
B
== (p ~ q) A
q == -'P B -.q
P
B
q =. (p A q) V (-.p A -.q)
-'(p
== p ~ (q A r )
== (p V q) ~ r
== p ~ (q V r)
== (p A q) ~ r
--
q
B
q)
== P
B
(q ~ p)
-.q