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