Section 12.2 – And, Or, and
Not, in Logic
Compound statement – when 2 or more statements are connected.
- A compound statement is either
true or false.
Conjunction 
– a compound statement that uses the word “and” to connect simple statements.
A conjunction is true iff both statements are true. If one or both of the statements are false, the conjunction is false.
Truth table – a table that lists all possible combinations of truth values for a given statement or combination of statements.
|
p |
q |
p
and q |
|
T |
T |
T |
|
T |
F |
F |
|
F |
T |
F |
|
F |
F |
F |
Disjunction 
– a compound statement that uses the word “or” to connect simple statements.
A disjunction is false iff both statements are false. If one or both of the statements are true, the disjunction is true.
Exclusive or – one or the other, but not both
Inclusive or – one or the other, or both
|
p |
q |
p
or q |
|
T |
T |
T |
|
T |
F |
T |
|
F |
T |
T |
|
F |
F |
F |
Negations ~
- if p is a statement, then not p is its negation.
|
p |
~p |
|
T |
F |
|
F |
T |
DeMorgan’s Laws
|
p |
q |
p |
~
(p |
|
T |
T |
|
|
|
T |
F |
|
|
|
F |
T |
|
|
|
F |
F |
|
|
|
p |
q |
~p |
~ q |
~p |
|
T |
T |
|
|
|
|
T |
F |
|
|
|
|
F |
T |
|
|
|
|
F |
F |
|
|
|
When 2 logic statements have the same truth values, they are
said to be truth functionally
equivalent.
~ (p q) ó ~p ~q