Compound Propositions and Truth Tables
Compound propositions:
Connective | Pronounced | Symbol in Logic |
Negation | NOT | ¬, ~, ‘ |
Conjunction | AND | Λ |
Disjunction | OR | V |
Conditional | if then | → |
Biconditional | if and only if | |
Exclusive or | either…or but not both |
Truth tables of Compound propositions:
a. Negation (NOT , ~ , ¬ , ‘ )
P |
~P |
T |
F |
F |
T |
b. Conjuction ( AND , Ʌ)
P |
Q |
PɅQ |
T |
T |
T |
T |
F |
F |
F |
T |
F |
F |
F |
F |
c. Disjunction (inclusive OR) (OR , V)
P |
Q |
PVQ |
T |
T |
T |
T |
F |
T |
F |
T |
T |
F |
F |
F |
d. Conditional, known also as implication (→)
P |
Q |
P→Q |
T |
T |
T |
T |
F |
F |
F |
T |
T |
F |
F |
T |
e. Biconditional ()
P |
Q |
PQ |
T |
T |
T |
T |
F |
F |
F |
T |
F |
F |
F |
T |
f. Exclusive OR ()
P |
Q |
P Q |
T |
T |
F |
T |
F |
T |
F |
T |
T |
F |
F |
F |