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)
If a person is not a musician, then the person is not a banjo player.
If a person is not a banjo player, then the person is a musician.
If a person is not a banjo player, then the person is not a musician.
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.

Z is the contrapositive of X.
Z is the converse of X.
Z is the inverse of X.
Z is the retrograde of X.

Answer 1

The correct answers are:

#3) If a person is not a musician, then the person is not a banjo player.

#4) Z is the inverse of X.

Step-by-step explanation:

The contrapositive of a statement is formed by switching the hypothesis and the conclusion of a statement, and then negating both.

The hypothesis of a statement comes after "if," and the conclusion comes after "then." The hypothesis of our statement is "a person is a banjo player" and the conclusion is "the person is a musician." Switching these makes "If a person is a musician, then the person is a banjo player." Negating each of them makes "If a person is not a musician, then the person is not a banjo player."

#4) The two pieces of the statement, hypothesis and conclusion, are in the same position, but both are negated. The inverse is formed by negating both the hypothesis and the conclusion.

Answer 2

"If a person is not a musician, then the person is not a banjo player" is the statement among the choices given in the question that is the contrapositive of the given statement. The correct option is the second option.

"Z is the inverse of X" is the way the two statements given below related to each other. The correct option is the third option.