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

Answer 1

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.

Explanation:

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 linear functions do not intersect at exactly one point.

This is because the contrapositive of an implication is logically equivalent to the original implication. The contrapositive of q→ p is ¬p→ ¬q, which means:

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

Simplifying this statement, we get:

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.