8
QuizMultiple Choice

Compound Statements

Question 8 • AZ-Common Core Algebra II A

Given:p: Two linear functions have different coefficients of x.q: The graphs of two functions intersect at exactly one point. Which statement is logically equivalent to q → p?

Answer
A
If two linear functions have different coefficients of x, then the graphs of the two functions intersect at exactly one point.
B
If two linear functions have the same coefficients of x, then the graphs of the two linear functions do not intersect at exactly one point.
C
If the graphs of two functions do not intersect at exactly one point, then the two linear functions have the same coefficients of x.
D
If the graphs of two functions intersect at exactly one point, then the two linear functions have the same coefficients of x.

Explanation

The implication q → p says: if the graphs intersect at exactly one point, then the linear functions have different coefficients of x. An equivalent statement is its contrapositive: if the functions do not have different coefficients of x, then the graphs do not intersect at exactly one point. Not having different coefficients means having the same coefficients, which is choice B.

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