Question

2. Mrs. Fiorina wrote the following statement on the board.

"A ray can be part of a line."
A group of students was discussing the meaning of this statement. They were
arguing back and forward about whether the converse of the statement is also
true. Jahmiah, the leader of the group, determined that the converse is not true.
Is Jahmiah correct or not? Justify your answer.

Answer 1

• Jahmiah is correct, the converse of the statement is not true.

Step-by-step explanation:

A conditional statement can be represented by p → q, meaning that if p is true then q is true.

The converse of the conditional statement p → q is q → p.

The converse of a statement may or may not be a true.

For the statement "A ray can be part of a line" the converse would be "A line can be part of a ray".

By definition, a ray is a part of a line with a start point that extends infinetly in one direction (it does not have end point).

By definition, a line has not a start point, it extends infinetly in two directions.

Hence, a ray is a part of a line but a line is not a part of a ray, which means that the converse of the given statement is not true, such as Jahmaiah has determined.