Question

select all the conditionals and truth values implied by the following biconditional. two lines are parallel if and only if they do not intersect. a. if two lines are parallel, then they do not intersect; t b. if two lines are not parallel, then they intersect; f c. if two lines do not intersect, then they are parallel; t d. if two lines intersect, then they are parallel; f e. if two lines intersect, then they are not parallel; t

Explanation:

A biconditional statement "p if and only if q" implies four conditional statements: "if p then q", "if q then p", "if not p then not q", and "if not q then not p". In a plane, two lines are parallel if and only if they do not intersect.

• For A: If two lines are parallel, they don't intersect, which is true in a plane.
• For B: In 3 - D space, two non - parallel lines may not intersect (skew lines), so "if two lines are not parallel, then they intersect" is false.
• For C: In 3 - D space, two non - intersecting lines may not be parallel (skew lines), so "if two lines do not intersect, then they are parallel" is false in 3 - D, but true in a plane. Assuming a 2 - D context here, it is considered true.
• For D: Intersecting lines cannot be parallel, so it's false.
• For E: Intersecting lines are not parallel, which is true.

Answer:

A. If two lines are parallel, then they do not intersect; T
C. If two lines do not intersect, then they are parallel; T
D. If two lines intersect, then they are parallel; F
E. If two lines intersect, then they are not parallel; T