Test the following statement to see if it is reversible. If so, choose the true biconditional. Parallel planes are planes that do not intersect. Planes are parallel if and only if they do not intersect. Planes that do not intersect are parallel planes. This statement is not reversible. Planes that intersect are not parallel planes
The statement is not reversible.
The true biconditional would be: "Planes are parallel if and only if they do not intersect."
To test the statement for reversibility, we need to check if it can be written in the form "if and only if" (p ⇔ q). However, the given statement is not reversible since it cannot be written in that form.
The original statement is: "Parallel planes are planes that do not intersect."
To rephrase it as a true biconditional, we can write: "Planes are parallel if and only if they do not intersect."
So, the true biconditional form of the statement is: "Planes are parallel if and only if they do not intersect."
To test the reversibility of a statement, we need to see if the inverse statement is also true. The inverse of the statement "Parallel planes are planes that do not intersect" is "Planes that intersect are not parallel planes."
To determine if the inverse statement is true, we need to evaluate if all planes that intersect are indeed not parallel. If we find one instance where intersecting planes are still parallel, then the inverse statement is false, and the original statement is not reversible.
Consider two planes: Plane A and Plane B. If they intersect at a single point, they are not considered parallel. However, if Plane A and Plane B are parallel, they will not intersect. This confirms that the inverse statement is true, and thus, the original statement is reversible.
So, the true biconditional for the statement "Parallel planes are planes that do not intersect" is "Planes are parallel if and only if they do not intersect."