Determine whether the conditional and its converse are both true. If both are true, combine them as a biconditional. If either is false, provide a counterexample.

If two lines are parallel, they do not intersect.
If two lines do not intersect, they are parallel.

Question

Determine whether the conditional and its converse are both true. If both are true, combine them as a biconditional. If either is false, provide a counterexample.

If two lines are parallel, they do not intersect.
If two lines do not intersect, they are parallel.

anonymous · Answer

One statement is false. If two lines do not intersect, they could be skew.
	Both statements are true. Two lines are not parallel if and only if they do not intersect.
	One statement is false. If two lines are parallel, they may intersect twice.
	Both statements are true. Two lines are parallel if and only if they do not intersect.