Q3 - Geometry

Question

Reword the following statement as two statements, one describing the existence and the other describing uniqueness:

A segment has exactly one midpoint.

Step-by-Step Solution

Answer

All segments have a midpoint states the existence and a segment that has only one midpoint that states the uniqueness.

Step 1. Existence and uniqueness.

The property of being the one and only object satisfying a certain condition is referred to as "uniqueness" and "existence" which is a weaker form of uniqueness, refers to the property that an object satisfying a property is "unique" only in the sense that all objects satisfying the property are equivalent to each other.

Step 2. State the Existence.

A statement describing Existence is: “All segments have a midpoint.”

Step 3. State the uniqueness.

A statement describing Uniqueness is: “A segment has only one midpoint.”

 

Hence, the answer is “All segments have a midpoint states the existence and a segment has only one midpoint that states the uniqueness.”