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A compound
sentence is formed when
two or more thoughts are connected in one
sentence.
The following are examples
of compound sentences:
- "21 is
divisible by 3
and 21 is not prime."
- "45 is a
multiple of 9
or 13 - 20 = 7."
- "If
4 + 6 = 10
and 3 + 3 = 9,
then all
rectangles are squares."
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When attempting to
determine the truth value of a compound sentence,
first determine the
truth value of each of the components of the sentence.
Let's examine
the examples listed above.
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1.
Determine the truth value
of:
"21
is divisible by 3
and
21 is not prime." |
| |
"21 is divisible by 3"
(true)
"21 is not prime"
(true)
|
|
|
Substitute the truth values for the facts: |
|
T and T |
 |
|
Simplify the conjunction (and): |
|
T
|
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Answer:
The compound sentence (statement) is true. |
|
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2.
Determine the truth value
of:
"45
is a multiple of 9
or
13 - 20 = 7." |
|
"45
is a multiple of 9"
(true)
"13
- 20 = 7"
(false)
| Substitute the
truth values for the facts: |
|
T
or F |
 |
| Simplify the
disjunction (or): |
|
T |
|
Answer:
The compound sentence (statement) is true. |
|
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3.
Determine the truth value
of:
"If
4 + 6 = 10
and
3 + 3 = 9,
then
all rectangles are squares." |
|
"4
+ 6 = 10 "
(true)
"3
+ 3 = 9"
(false)
"all
rectangles are squares."
(false)
| Substitute the
truth values for the facts: |
|
if
(T and F) then F |
| Simplify the
conjunction (AND) first: |
|
if
F then F |
| Simplify the
conditional: |
|
T
|
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Answer:
The compound sentence (statement) is true. |
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