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.
D
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.

Answer 1

The statement that is logically equivalent to q-p is:

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

This is the contrapositive of the original statement q-p, which is logically equivalent to the statement itself. In other words, if we negate both p and q, and switch their order, we obtain the contrapositive statement that is also logically equivalent to q-p.