p q Negation
p Conjunction p q Disjunction p q Conditional p → q Biconditional p q
T T F T T T T
T F F F T F F
F T T F T T F
F F T F F T T
Not p
Opposite
truth values
from p
p or q
False only when
BOTH p and q
are false
p and q
True only when
BOTH p and q
are true
If p, then q
False only when
p is true and q
is false
If and only if p,
then q
True only when
p and q have
the same truth
value
p q
Two statements are equivalent if they have the same truth value in all cases.
Variations of the Conditional Statement p → q
• p → q is equivalent to q → p, the contrapositive:
p → q q → p
• p → q is NOT equivalent to q → p, the converse
• p → q is NOT equivalent to p → q, the inverse
• The negation of p → q is p q: (p → q) p q
De Morgan’s Laws
• (p q) p q:
The negation of p q is p q
• (p q) p q:
The negation of p q is p q
T R U T H T A B L E A N D L O G I C R EFERENCE S H E E T
