Chapter 1B - Propositions and Truth Values
A proposition is a set of statements that make a distinct assertion or denial (which may be true or
false) and must be in the form of a complete sentence.
Any proposition has two possible values True (T) or False (F). The negation of a proposition p is
the proposition (denoted ∼ p) that makes the opposite of p.
A Truth Table is a table with a row for each possible set of truth values for the proposition being
considered.
Negation, ∼ (Not)
AND, ∧, (Conjunction) (only true if both p and q are true)
OR, ∨, (Disjunction) (Inclusive either or both) (Exclusive
one or the other but not both) In Logic assume Inclusive
(always true unless both p and q are false)
IF ... THEN , statements (Conditionals) (Conditional is
true unless p is true and q is false)
Name
Form
Conditional
if p, then q
Converse
if q, then p
Inverse
if ∼ p, then ∼ q
Contrapositive
if ∼ q, then ∼ p
p
∼p
T
F
F
T
p
q
p and q
T
T
F
F
T
F
T
F
T
F
F
F
p
q
p or q
T
T
F
F
T
F
T
F
T
T
T
F
p
q
if p, then q
T
T
F
F
T
F
T
F
T
F
T
T
Two statements are Logically Equivalent if the have the same truth values, i.e., one is true if and only
if the other is true. The conditional and contrapositive are logically equivalent and the Converse
and Inverse are logically equivalent.