Question
Determine Whether the conditional and its converse are both true.?
If both are true, then 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) One statement is false. If two lines do not intersect, they could be skew.
b) Both statements are true. Two lines are not parallel if and only if they do not intersect.
c) One statement is false. If two lines are parallel, they may intersect twice.
d) Both statements are true. Two lines are parallel if and only if they do not intersect.
Answer
a) is the correct answer.
If both lines lie in the same plane then the answer would be
d) Both statements are true. Two lines are parallel if and only if they do not intersect.
If both lines do not lie in the same plane then the answer would be
a) One statement is false. If two lines do not intersect, they could be skew.
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