Given a conditional βIf P then Q,β the inverse is formed by negating both the antecedent and the consequent while keeping their order: βIf not P then not Q.β Here, P is βthe student is sincereβ and Q is βthe student passes the exam.β The inverse is therefore βIf a student is not sincere, then the student does not pass the exam.β
Option A:
Option A is the converse, reversing the roles of antecedent and consequent to βIf Q then P.β
Option B:
Option B correctly negates both antecedent and consequent without swapping them, matching the standard definition of the inverse.
Option C:
Option C negates only the antecedent while leaving the consequent positive, which does not correspond to any standard paired form (it is neither converse, inverse, nor contrapositive of the original).
Option D:
Option D is the contrapositive, βIf not Q then not P,β which is logically equivalent to the original conditional, not its inverse.
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