Question

3. Which statement is the contrapositive of the given statement?

If a person is a banjo player, then the person is a musician. (1 point)
A) If a person is not a musician, then the person is not a banjo player.
B) If a person is not a banjo player, then the person is a musician.
C) If a person is not a banjo player, then the person is not a musician.
D) If a person is a musician, then the person is not a banjo player.

4. How are the two statements given below related to each other?
X: If you run for 10 minutes, then you will raise your heart rate.
Z: If you do not run for 10 minutes, then you will not raise your heart rate. (1 point)
A) Z is the contrapositive of X.
B) Z is the converse of X.
C) Z is the inverse of X.
D) Z is the retrograde of X.

Answer 1

3) A contrapositive is formed by negating the hypothesis and the conclusion and switching their positions. So,
"If a person is a banjo player, then the person is a musician"
First we negate:
"If a person is not a banjo player, then the person is not a musician"
And then we switch:
"If a person is not a musician, then the person is not a banjo player"
The answer is A
4) Both the hypothesis and conclusion of X have been negated in Z, so Z is the inverse of X. Thus the answer is C.