When would the following conditional be false?
If you work 20 hours a week, then you make $125.00.
(1 point)
Responses
You work 25 hours a week, and make $125.00.
You work 25 hours a week, and make $125.00.
You work 25 hours a week, and you make $175.00.
You work 25 hours a week, and you make $175.00.
You work 20 hours a week, and you make $175.00.
You work 20 hours a week, and you make $175.00.
You work 20 hours a week, and you make $125.00.
In a conditional statement, which is often structured in the form "If P, then Q," the statement is considered false only when P is true and Q is false. This is because the statement is asserting that whenever P happens, Q will also happen; therefore, if P happens without Q, the statement has been proven false.
Let's evaluate each response with respect to the original conditional statement, "If you work 20 hours a week, then you make $125.00."
1. You work 25 hours a week, and make $125.00.
This response does not make the conditional statement false, because the condition (working 20 hours a week) is not satisfied. The statement makes no claims about working any other number of hours.
2. You work 25 hours a week, and you make $175.00.
Again, this response does not make the conditional statement false, as it still does not satisfy the condition of working 20 hours a week.
3. You work 20 hours a week, and you make $175.00.
This response could potentially make the statement false if we interpret the statement to mean you can only make exactly $125.00 when working 20 hours a week and not a dollar more. However, if the statement allows for making at least $125.00, then this situation would not make the statement false.
4. You work 20 hours a week, and you make $125.00.
This response is consistent with the conditional statement and thus does not make it false. The condition is met (working 20 hours a week), and the result is as expected (making $125.00).
If the original statement is strictly interpreted (meaning you make exactly $125 and no more when you work 20 hours), then the response that makes the conditional statement false would be:
You work 20 hours a week, and you make $175.00.
If the statement is meant to say that you will make at least $125 but possibly more, then none of the responses provided make the statement false.