Question

given: • p: student achieves 90 percent on the geometry final. • q: student will receive a passing grade in geometry class. which statement is logically equivalent to q → p? if a student achieves 90 percent on the geometry final, then the student will pass geometry class. if a student passes geometry class, then the student achieved 90 percent on the geometry final. if a student did not pass geometry class, then the student did not achieve 90 percent on the geometry final. if a student did not achieve 90 percent on the geometry final, then the student did not pass geometry class.

Explanation:

Step1: Recall logical equivalence rules

The contra - positive of a conditional statement $q
ightarrow p$ is $
eg p
ightarrow
eg q$. A conditional statement and its contra - positive are logically equivalent.

Step2: Identify the components

Given $q$: student will receive a passing grade in geometry class and $p$: student achieves 90 percent on the geometry final. Then $
eg p$ is student did not achieve 90 percent on the geometry final and $
eg q$ is student did not pass geometry class.

Step3: Form the contra - positive

The contra - positive $
eg p
ightarrow
eg q$ is "If a student did not achieve 90 percent on the geometry final, then the student did not pass geometry class".

Answer:

If a student did not achieve 90 percent on the geometry final, then the student did not pass geometry class.