Question

unit 3 - logic and geometry
11 of 34
this quiz: 34 point(s) pos
this question: 1 point(s)
write the converse, inverse, and contrapositive of the statement.
if you wash the car, then you can drive it.

identify the converse statement.
a. if you cannot drive it, then you did not wash the car.
b. if you can drive it, then you wash the car.
c. if you did not wash the car, then you cannot drive it.
d. if you cannot drive it, then you wash the car.

identify the inverse statement.
a. if you can drive it, then you wash the car.
b. if you cannot drive it, then you wash the car.
c. if you did not wash the car, then you cannot drive it.
d. if you cannot drive it, then you did not wash the car.

identify the contrapositive statement.
a. if you cannot drive it, then you did not wash the car.
b. if you can drive it, then you wash the car.
c. if you did not wash the car, then you cannot drive it.
d. if you cannot drive it, then you wash the car.

Explanation:

Converse Statement

The original statement is "If you wash the car (let \( p \) be "you wash the car"), then you can drive it (let \( q \) be "you can drive it")", so \( p \to q \). The converse of a conditional statement \( p \to q \) is \( q \to p \), which means "If you can drive it, then you wash the car". Looking at the options, option B matches this.

The inverse of a conditional statement \( p \to q \) is \(
eg p \to
eg q \), where \(
eg p \) is "you did not wash the car" and \(
eg q \) is "you cannot drive it". So the inverse should be "If you did not wash the car, then you cannot drive it", which is option C.

The contrapositive of a conditional statement \( p \to q \) is \(
eg q \to
eg p \), where \(
eg q \) is "you cannot drive it" and \(
eg p \) is "you did not wash the car". So the contrapositive should be "If you cannot drive it, then you did not wash the car", which is option A.

Answer:

B. If you can drive it, then you wash the car.

Inverse Statement