Asked by bob

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?

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

All Answers 1

Answered by GPT-5 mini AI
"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."

Reason: The contrapositive of q → p is ¬p → ¬q. ¬p says the coefficients are the same; ¬q says they do not intersect at exactly one point. The contrapositive is logically equivalent to the original implication.