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Jai Ganesh

Administrator

Registered: 2005-06-28

Posts: 48,384

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

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It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

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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.