Question

The contrapositive of the statement
“If two lines do not intersect in the same plane then they are parallel.” is

• A. If two lines are not parellel then they do not intersect in the same plane.
• B. If two lines are not parallel then they intersect in the same plane.
• C. If two lines are parellel then they do not intersect in the same plane.
• D. If two lines are parallel then they intersect in the same plane.

Hint:

To form the contrapositive of a statement, negate both the hypothesis and conclusion, then swap them. For example, the contrapositive of "If P, then Q" is "If not Q, then not P." This is important when reasoning logically about statements and their inverses.

Answer 1

The Correct Option is B

The correct answer is (B) : If two lines are not parallel then they intersect in the same plane.

Answer 2

The correct answer is: (B) If two lines are not parallel then they intersect in the same plane.

We are given the statement: "If two lines do not intersect in the same plane, then they are parallel." The contrapositive of a statement is formed by negating both the hypothesis and the conclusion, and then swapping them.

The original statement is in the form of:

"If P, then Q."

where:

• P: Two lines do not intersect in the same plane.
• Q: The lines are parallel.

The contrapositive is formed by negating both P and Q and swapping them:

"If not Q, then not P."

In this case:

• Not Q: The lines are not parallel.
• Not P: The lines intersect in the same plane.

So, the contrapositive of the given statement is: "If two lines are not parallel, then they intersect in the same plane." Therefore, the correct answer is (B) If two lines are not parallel then they intersect in the same plane.