Questions: Is the following statement true or false? A plane is one-dimensional. true false

Solution Steps

To determine if the statement "A plane is one-dimensional" is true or false, we need to understand the basic properties of geometric dimensions. A plane is a flat, two-dimensional surface that extends infinitely in all directions. Therefore, the statement is false.

A plane is a fundamental concept in geometry. It is defined as a flat, two-dimensional surface that extends infinitely in all directions. The key characteristic of a plane is its dimensionality.

The statement in question is: "A plane is one-dimensional." To evaluate this, we compare the dimensionality of a plane with the given statement. A plane is two-dimensional, which can be expressed as: \[ \text{Dimensions of a plane} = 2 \]

Since the statement claims that a plane is one-dimensional, we compare: \[ \text{Is the plane one-dimensional?} \] \[ 2 \neq 1 \]

The statement is false because a plane is not one-dimensional; it is two-dimensional.

Final Answer