Final answer:
The conjecture 'Lewis can go to college' is valid according to the Law of Detachment because the given statements establish that if Lewis earns a scholarship, he can attend college, and it is stated that Lewis did earn a scholarship.
Step-by-step explanation:
The Law of Detachment in logic says that if a conditional statement 'if P, then Q' is accepted, and the antecedent P is true, then the consequent Q must also be true. In the given scenario, we have two statements: 'If Lewis earns a scholarship (P), he can go to college (Q)', and 'Lewis earns a scholarship (P)'.
According to the Law of Detachment, since the antecedent (Lewis earning a scholarship) is true, the consequent (Lewis can go to college) must also be true. Therefore, the conjecture 'Lewis can go to college' is indeed valid based on the Law of Detachment.