Question

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.

Answer 1

The second statement.

Reason: q → p is equivalent to its contrapositive ¬p → ¬q. Here ¬p = "the two linear functions have the same coefficient of x" and ¬q = "the graphs do not intersect at exactly one point", which is exactly the second statement. The first statement is the converse (p → q) and is not the same as q → p in general.