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 \Leftrightarrow
Exclusive or either…or but not both \oplus

 

 

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

PQ

T

T

T

T

F

F

F

T

T

F

F

T

 

e.       Biconditional (\Leftrightarrow) 

P

Q

P\LeftrightarrowQ

T

T

T

T

F

F

F

T

F

F

F

T

 

f.      Exclusive OR (\oplus

P

Q

\oplusQ

T

T

F

T

F

T

F

T

T

F

F

F

 

 

 

 

 

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