To determine whether each sentence is a mathematical statement or not, we will analyze them individually. A mathematical statement is a sentence that is either true or false but not both. Opinions or subjective sentences are not considered mathematical statements.
1. Diagonals of a square are perpendicular.
- This is a mathematical statement because it can be proven to be either true or false. In fact, this is true because in a square, diagonals bisect each other at right angles (90 degrees).
2. Graphs with three-digit numbers look better.
- This is not a mathematical statement. It is subjective and based on opinion or personal preference. It cannot be conclusively proven to be either true or false.
3. Polygons are more useful than circles.
- This is not a mathematical statement. It is subjective and involves personal opinion about the usefulness, which can't be quantified or proven unequivocally as true or false.
4. Prime numbers have no divisors.
- This is a mathematical statement because it can be proven to be true or false. Prime numbers are defined as natural numbers greater than 1 that have no positive divisors other than 1 and themselves. Therefore, the statement is true if interpreted correctly as "Prime numbers have no proper divisors."
5. The sum of two negative numbers is a positive number.
- This is a mathematical statement because it can be proven false. The sum of two negative numbers is always a negative number, so the statement is incorrect.
Based on this analysis, we can categorize the sentences as follows:
### Mathematical Statements:
- Diagonals of a square are perpendicular.
- Prime numbers have no divisors.
- The sum of two negative numbers is a positive number.
### Not Mathematical Statements:
- Graphs with three-digit numbers look better.
- Polygons are more useful than circles.
