Question

What form of deductive reasoning is used in the given argument? If a number ends in 0, then it is divisible by 10. If a number is divisible by 10, then it is divisible by 5. If a number ends in 0, then it is divisible by 5. A. Law of detachment B. Law of syllogism C. Law of contrapositive D. Identification of counterexample

Answer 1

Answer:

B. Law of syllogism.

Explanation:

The deductive reasoning behind the set of arguments is the Law of Syllogism, defined by the following logical rule:

1) $\alpha \Rightarrow \beta$

2) $\beta \Rightarrow \gamma$

Hence,

3) $\alpha \Rightarrow \gamma$

In this case, we have three simple propositions:

$\alpha =$ A number ends in 0.

$\beta =$ A number is divisible by 10.

$\gamma =$ A number is divisible by 5.

The reasoning represented by the consecutive arguments is:

1) If a number ends in 0, then it is divisible by 10.

2) If a number is divisible by 10, then it is divisible by 5.

Hence,

3) If a number ends in 0, then it is divisible by 5.