|
|
In
logic, a disjunction is a compound
sentence formed by combining two sentences (or facts) using the
word "or."
A disjunction is true
when EITHER or BOTH
sentences (or facts) are true. |
Examples:
|
1.
|
"Blue is a
color
or
7 + 3 = 10."
(T
or
T =
T) Since both facts are true, the entire sentence is true.
|
| 2. |
"One
hour = exactly 55 minutes or one minute =
exactly 60 seconds."
(F or
T = T) Since the second fact is true,
the entire sentence is true.
|
| 3. |
"3
+ 4 = 6 or all dogs meow."
(F or F
= F) Since both facts are false, the entire sentence is false.
|
| 4. |
"The word cat has 3 letters or the
word dog has four letters."
(T
or F = T) Since the first fact is true,
the entire sentence is true.
|
|
Mathematicians
often use symbols and tables to represent concepts in logic.
The use of these variables, symbols and tables creates a shorthand
method for discussing logical sentences.
|
Truth
table for disjunction (or):
(notice the
symbol used for "or" in the table below)
|
A
truth table is a pictorial
representation of all of the possible outcomes of the
truth value of a compound sentence. Letters such as
 and
are used to represent the facts (or sentences) within the
compound sentence. |
|
Remember:
|
For a disjunction (or) to be true,
EITHER or BOTH facts must
be true.
|
 |
|
|
