Which conditional completes the Law of Syllogism? If p → q and _____ are true statements, then p → r is a true statement. 1. p → r 2. r → q 3. q → r 4. q → p
The correct conditional that completes the Law of Syllogism is option 4: q → p.
The correct conditional that completes the Law of Syllogism is option 3: q → r.
To complete the Law of Syllogism, we need to find the correct conditional statement that would make the statement "If p → q and _____ are true statements, then p → r is a true statement" true.
The Law of Syllogism states that if p → q and q → r are both true statements, then p → r is also a true statement.
In this case, we are given that p → q is true. So, we need to find a statement that, when combined with p → q, gives us q → r.
Looking at the answer choices:
1. p → r: This is not what we are looking for. We are given p → q, not p → r.
2. r → q: This is not what we are looking for either. We need the statement that when combined with p → q, gives us q → r.
3. q → r: This is the correct choice. If we combine p → q and q → r, we can conclude p → r.
4. q → p: This is not what we are looking for. We need the statement that when combined with p → q, gives us q → r.
Therefore, the conditional that completes the Law of Syllogism in this case is option 3: q → r.