Show that subtraction and division are not binary operations on N.

Explanation

To show that subtraction and division are not binary operations on the set of natural numbers \( \mathbb{N} \), we need to understand the definition of a binary operation. A binary operation on a set \( S \) is a function that takes two elements from \( S \) and produces another element from \( S \).

### Step 1: Show that subtraction is not a binary operation on \( \mathbb{N} \)

1. **Select Elements**: Let \( A, B \in \mathbb{N} \).
2. **Perform Subtraction**: Consider \( A - B \).
3. **Check Conditions**:
- If \( A \geq B \), then \( A - B \) is a natural number.
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