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.

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

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.

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

agent0smith · Answer

hmm... I don't really know what skew lines are, so: http://mathworld.wolfram.com/SkewLines.html

agent0smith · Answer

Two lines in the 3 dimensional plane can not intersect, but also not be parallel.

agent0smith · Answer

C: One statement is false. If two lines do not intersect, they could be skew.