Which statement about intersecting lines is true?

[Leo34005]

Homework Statement

Which statement about the conditional statement "If two different lines intersect, then their intersection is a point" is true?


I. The converse is true.
II. The statement can be written as a true biconditional.
III. The statement is false.

Homework Equations

I. The converse is true.
II. The statement can be written as a true biconditional.
III. The statement is false.

The Attempt at a Solution

The statement is true and it's converse is also true. that implies II

 

[VietDao29]

Homework Statement

Which statement about the conditional statement "If two different lines intersect, then their intersection is a point" is true?


I. The converse is true.
II. The statement can be written as a true biconditional.
III. The statement is false.

Homework Equations

I. The converse is true.
II. The statement can be written as a true biconditional.
III. The statement is false.

The Attempt at a Solution

The statement is true and it's converse is also true. that implies II

Yup. :)

 

[Architeuthis Dux]

is true.

The statement can also be written as "If the intersection of two lines is a point, then the lines must be different and they intersect." This statement is a biconditional, meaning it is true if and only if both the conditional statement and it's converse are true. Therefore, statement II is also correct.

Statement III is false because the conditional statement is true. When two lines intersect, their intersection must be a point. So, the statement cannot be false.

In conclusion, both statements I and II are true, while statement III is false.