Write the negative of the following statement : "Some students are 25 (years) or older"

Answer

To write the negative of the statement "Some students are 25 years or older," we need to understand the implications of the original statement and how to negate it logically.

### Step-by-Step Solution:

1. **Understand the Original Statement**:
The statement "Some students are 25 years or older" implies that there exists at least one student who is either 25 years old or older.

2. **Identify the Logical Structure**:
The statement can be expressed in logical terms as:
- There exists (∃) a student (S) such that S is 25 years or older.

3. **Negate the Statement**:
To negate the statement, we need to express that it is not true that some students are 25 years or older. In logical terms, this can be expressed as:
- It is not the case that there exists a student such that the student is 25 years or older.

4. **Rephrase the Negation**:
The negation can be rephrased to say:
- All students are younger than 25 years.
- Alternatively, we can say:
- None of the students are 25 years old or older.

5. **Final Answer**:
Therefore, the negative of the statement "Some students are 25 years or older" can be written as:
- "All students are under 25 years of age."
- Or, "None of the students are 25 years or older."