Question

use the law of syllogism to determine a valid conclusion from the set of statements, if possible. select valid conclusion or no valid conclusion and explain your reasoning.
if a number ends in 0, then it is divisible by 2.
if a number ends in 4, then it is divisible by 2.
select choice
select choice

Explanation:

Step1: Analyze the Law of Syllogism

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's define the statements:

• Let \( p_1 \): "a number ends in 0", \( q_1 \): "it is divisible by 2" (so \( p_1 \to q_1 \))
• Let \( p_2 \): "a number ends in 4", \( q_2 \): "it is divisible by 2" (so \( p_2 \to q_2 \))

Step2: Check for Syllogism Application

For the Law of Syllogism, the consequent of the first statement must be the antecedent of the second. Here, the consequent of both statements is "it is divisible by 2" (\( q_1 = q_2 \)), but the antecedents are different (\( p_1
eq p_2 \)). So there's no chain (like \( p \to q \) and \( q \to r \)) to apply the Law of Syllogism between these two statements. Thus, no valid conclusion can be drawn by combining these two using the Law of Syllogism.

Answer:

No valid conclusion can be drawn using the Law of Syllogism because the two conditional statements do not form a chain (the consequent of one is not the antecedent of the other; both have the same consequent "divisible by 2" but different antecedents "ends in 0" and "ends in 4").