4
QuizMultiple Choice

Conditional Statements and Equivalence

Question 4 • (A. Costello)WCA 5324 Geometry 1st Nine Weeks 26-27

What is the contrapositive of the conditional statement?If two variables are directly proportional, then their graph is a linear function.

Answer
A
If two variables are directly proportional, then their graph is not a linear function.
B
If two variables are not directly proportional, then their graph is not a linear function.
C
If the graph of two variables is a linear function, then the two variables are directly proportional.
D
If the graph of two variables is not a linear function, then the two variables are not directly proportional.

Explanation

Let p be “the variables are directly proportional” and q be “their graph is a linear function.” The contrapositive of p → q is not q → not p: reverse the two parts and negate each one. So the contrapositive is “If the graph is not a linear function, then the variables are not directly proportional,” which is choice D.

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