A proposition (a.k.a statement) is a declarative sentence that is either true [T] or false [F], but
not both. T and F are called truth values.
A predicate has an unknown variable.
Which of the following is a proposition?
1. Atlanta is the capital of Florida. Yes: False
2. George Washington wore red boots at least once. Yes: Either
3. She is a tennis player. No: Predicate
4. Forget about it. No: not declarative
5. Today is Thursday and it is sunny. Yes: False
6. 2x > 4. No: Predicate
7. This sentence is false. Paradoxal, self reference “this”
Compound Statements
A simple proposition is a proposition that does not contain other propositions as parts.
A compound proposition is a proposition constructed from other propositions by the use of
logic operations (connectives) described below.
Name
Meaning
Notation
Negation
Not p
¬p or ~q
Conjuction
p and q
(p ∧ q) or (p & q)
Disjunction
p or q
pVq
Conditional
If p then q
p→q
Biconditional
p if and only if q
p↔q
A propositional form is an expression made up of propositional variables (such as p, q, r) and
logical operations (connectives), such as (∧, v, ¬, →, ↔) that becomes a proposition when
actual propositions are substitute for the variables.
The truth table for the given propositional form displays the truth values that correspond to all
possible combinations of truth values for it propositional values.
Operator precedence:
¬ is evaluated first, then ∧, then v, then →, then ↔.