Question

select the correct answer.
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

Explanation:

The law of syllogism states that if we have two conditional statements \( p \to q \) and \( q \to r \), we can conclude \( p \to r \). Here, let \( p \) be "a number ends in 0", \( q \) be "it is divisible by 10", and \( r \) be "it is divisible by 5". The first statement is \( p \to q \), the second is \( q \to r \), and the conclusion is \( p \to r \), which matches the law of syllogism. The law of detachment requires a specific case of \( p \) to conclude \( q \), the law of contrapositive is about \(
eg q \to
eg p \), and identification of counterexample is about finding an example that disproves a statement, none of which apply here.

Answer:

B. law of syllogism