Which conditional completes the Law of Syllogism? If p → q and _____ are true statements, then p → r is a true statement. p → r r → q q → r q → p
If p → r and r → q are true statements, then p → q is a true statement.
The conditional that completes the Law of Syllogism is "q → r."
The conditional that completes the Law of Syllogism is q → r.
To understand why, let's break it down step by step:
1. The Law of Syllogism states that if there are two conditional statements and the conclusion of the first statement matches the hypothesis of the second statement, then the conclusion of the second statement can be inferred.
2. In this case, we have the conditional statement p → q, which means "if p, then q."
3. We want to determine if the statement p → r is true. The conclusion of this statement is r.
4. According to the Law of Syllogism, in order for p → r to be true, the conclusion of the first statement (p → q) should match the hypothesis of the second statement (q → r).
5. Therefore, the missing conditional to complete the Law of Syllogism is q → r.
In summary, if we have p → q and q → r as true statements, then we can use the Law of Syllogism to infer that p → r is also a true statement.