Symbols, formulas, truth tables that you need to know for the test
Connective
and
or
not
If …then
If and only if
Symbol
Λ
V
~
→
↔
Name
Conjunction
Disjunction
Negation
Implication
Biconditional
The 5 BASIC truth tables:
Negation, 'not p'
p
T
F
Conjunction, 'p and q'
p
T
T
F
F
~p
F
T
"T to F, F to T."
q
T
F
T
F
q
T
F
T
F
pΛq
T
F
F
F
p
T
T
F
F
"Only True if both are True."
Implication, 'If p, then q'
p
T
T
F
F
Disjunction, 'p or q'
p→q
T
F
T
T
"Only False if p is True and q is False."
q
T
F
T
F
pVq
T
T
T
F
"Only False if both are False."
Biconditional, 'p if and only if q'
p
T
T
F
F
q
T
F
T
F
p↔q
T
F
F
T
"Only True if p and q have the same truth value."
DeMorgan’s Laws
Alternate ways to write implications
~(p Λ q) ≡ ~p V ~ q
~(p V q) ≡ ~p Λ ~ q
p → q ≡ ~p V q
~(p → q) ≡ p Λ ~ q