5. What is the contrapositive of the following conditional:
"If a student plays basketball, then the student is over 6 feet tall."
A- If a student is over 6 feet tall then the student plays basketball.
B - IF a student is not over 6 feet tall, then the student does not play basketball.
C - If a student does not play basketball, then the student is not over 6 feet tall.
D - A student plays basketball if and only if the student is over 6 feet tall.
Would the answer be B?
B. If a student is not over 6 feet tall, then the student does not play basketball.
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Bingo! The answer is B. And just like a short basketball player trying to dunk, the contrapositive flips the original statement upside down. So, if "If a student plays basketball, then the student is over 6 feet tall" is the original statement, then the contrapositive would be "If a student is not over 6 feet tall, then the student does not play basketball." It's like saying, "If you can't reach the top shelf, then you can't have any cookies." No cookies for you!
Yes, the contrapositive of the conditional statement "If a student plays basketball, then the student is over 6 feet tall" is option B: "If a student is not over 6 feet tall, then the student does not play basketball."
To understand how to arrive at the contrapositive, first recognize that in a conditional statement of the form "if p, then q," the inverse would be "if not p, then not q." The contrapositive, on the other hand, flips the order and negates both components, resulting in "if not q, then not p."
In this case, the statement "If a student plays basketball, then the student is over 6 feet tall" can be rephrased as "If p (playing basketball), then q (being over 6 feet tall)." The negation of p is "not p (not playing basketball)," and the negation of q is "not q (not being over 6 feet tall)." Thus, the contrapositive becomes "If not q (not being over 6 feet tall), then not p (not playing basketball)," matching option B.