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#1 2007-11-09 23:57:54

ganesh
Moderator
Registered: 2005-06-28
Posts: 20,758

Symbolic Logic

Symbolic Logic

1. AND
Let p and q be two propositions.
Let the proposition 'p AND q' be denoted by p^q, called the conjunction.

0^0 = 0     
1^0 = 0     
0^1 = 0     
1^1 = 1     

TRUTH TABLE
p               q            p^q
T               T              T
T               F              F
F               T              F
F               F              F

2. OR
Let p and q be two propositions.
Let the proposition 'p OR q', be denoted by pvq, called disjunction.

0v0 = 0     
1v0 = 1
0v1 = 1     
1v1 = 1     

TRUTH TABLE
p                q              pvq
T               T                T
T               F                T
F               T                T
F               F                 F

3. NOT
Let p be the proposition. 'It is not the case that p', called negation, read as 'not p' be denoted by ~.
~0 = 1       
~1 = 0

TRUTH TABLE
p             ~p
T              F
F              T

Commutative Laws

p^q = q^p
pvq = qvp


Associative Laws

p^(q^r) = (p^q)^r
pv(qvr) = (pvq)vr


Distributive Laws

p^(q^r) = (p^q) v (p^r)
p^(qvr) = (pvq) ^ (pvr)


De Morgan's Laws

~(p^q) = ~p v ~q   NAND

~(pvq) = `p ^ ~q    NOR


It is no good to try to stop knowledge from going forward. Ignorance is never better than knowledge - Enrico Fermi. 

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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#2 2012-09-17 17:25:17

cool_jessica
Member
Registered: 2012-06-26
Posts: 15

Re: Symbolic Logic

Truth Table may seem a bit confusing in beginning but once you understand the concept of "0" and "1" things will become really easy. Just remember these set of rules and truth table will be one of the easiest subject to deal with.

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