Final answer:
The conclusion that if it is Monday, then Tyreke must take the bus is drawn using the Law of Syllogism, which combines two conditional statements to form a new conditional statement.
Step-by-step explanation:
The student's question involves determining whether the Law of Detachment or the Law of Syllogism was used to draw a conclusion from a given set of conditional statements. To solve this, let's examine the statements and the conclusion:
- If it is Monday, then Tyreke has football practice.
- If Tyreke has football practice, then he must take the bus.
- Conclusion: If it is Monday, then Tyreke must take the bus.
The Law of Syllogism, also known as the chain rule, allows us to combine two conditional statements where the conclusion of the first is the hypothesis of the second, to form a single conditional statement. Here, the first statement can be represented as If P, then Q, and the second as If Q, then R. Using the Law of Syllogism, we can then deduce If P, then R, which is the conclusion given: If it is Monday (P), then Tyreke must take the bus (R).
This kind of reasoning does not apply the Law of Detachment, since the Law of Detachment would require a statement directly asserting that it is indeed Monday (P is true), leading to the subsequent conclusion that Tyreke has football practice (Q is true).