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 \(
eg p
ightarrow
eg q\).

Step2: Identify the statements

\(p\): student achieves 90 percent on the geometry final. \(
eg p\): student did not achieve 90 percent on the geometry final. \(q\): student will receive a passing grade in geometry class. \(
eg q\): student did not pass geometry class.

Step3: Write the contra - positive

The contra - positive \(
eg p
ightarrow
eg q\) means "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.