Question

Given the following statements, which answer uses deductive reasoning to draw the conclusion?
If a number is even, then it is divisible by 2. g = 14.

A. The number is divisible by 2, therefore, the number is 14.

B. The number 14 is even and is greater than 2

C. The number 14 is even and therefore is divisible by 2.

D. The number 14 is a real number

Answer 1

Determine whether the stated conclusion is valid based on the given information. If not, write invalid. Explain your reasoning.
3. Given: If a number is divisible by 4, then the number is divisible by 2. 12 is divisible by four.
Conclusion: 12 is divisible by 2.
SOLUTION:
If p → q is a true statement and p is true, then q. Here, a number divisible 4 is divisible by 2 also and 12 is divisible by 4. So, 12 is divisible by 2 is a valid statement by the Law of Detachment.
ANSWER:
valid; Law of Detachment
4. Given: If Elan stays up late, he will be tired the next day. Elan is tired.
Conclusion: Elan stayed up late.
SOLUTION:
If p is true, then q is true, but q being true does not necessarily mean that p is true. Elan could be tired because he worked out. So, the statement is invalid.
ANSWER:
Invalid; Elan could be tired because he worked out.
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Answer 2

The statement which uses deductive reasoning to draw the conclusion is C. The number 14 is even and therefore is divisible by 2.

If a number is even, then it is divisible by 2. g = 14.

Which statement draws the conclusion?

The statement which shows the logical reasoning could be the correct one.

A. The number is divisible by 2, therefore, the number is 14.

Here any even number can be divisible by 2 other than 14.

B. The number 14 is even and is greater than 2. The given conclusion does not mention any number that is greater than 2.

C. The number 14 is even and therefore is divisible by 2. This is the correct statement.

D. The number 14 is a real number.

Learn more about reasoning function here:

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