|
In the above lessons,
you learned Logic
is the study of reasoning, and
it deals with statements that are either true or false. These
statements can be joined by the words:
and, or,
or not. When
attempting to determine the truth value of a
compound statement,
first determine the truth value (true
or false) of each of the components of
the sentence.
Remember a
compound
statement is formed when
two or more ideas are joined in one sentence.
The following are examples of
compound statements with all three connectors:
- "1
is an odd number
and
2 is an even number."
-
"15 - 5 = 10
or
10 + 2 = 17."
-
"It is
not
true
that:
5 + 3 = 8
and
4 x 2 = 6."
|
When deciding the truth
value of a compound statement, first
decide the truth value of each of the
components of the sentence.
Let's take a look at the examples listed above.
|
1. Decide the
truth value of: "1
is an odd number
and
2 is an even number." |
|
"1 is an odd
number" (true)
"2 is an even number."
(true)
Replace
the truth values for the facts: T and T
T +
T = T
Answer:
The compound statement
is true. |
|
2. Decide the
truth value of: "15
- 5 = 10 or 10 +2 = 17."
|
|
"15 - 5
= 10" (true)
"10 +2 = 17"
(false)
Replace
the truth values for the facts: T and F
T (or) F = T
Answer:
The compound statement
is true..
|
|
3.
Decide the
truth value of: "It is
not
true
that: 5 + 3 = 8
and
4 x 2 =
6."
|
|
"5 + 3 =
8"
(true)
"4 x 2 = 6"
(not
true)
Replace the truth values for the facts: T and T
T (and) T = T
Answer:
The compound statement
is true.
|
|
