Natural numbers are not closed under multiplication.
Why the statement is false (step by step):
Natural numbers are: \(1, 2, 3, 4, \ldots\)
What does “closed under multiplication” mean?
If we take any two natural numbers \(a\) and \(b\), their product \(a \times b\) should also be a natural number.
Check with examples:
Example 1: \(2 \times 3 = 6\). Here, \(2\) and \(3\) are natural, and \(6\) is also natural.
Example 2: \(4 \times 1 = 4\). Both \(4\) and \(1\) are natural, and \(4\) is natural.
Example 3: \(7 \times 9 = 63\). Both \(7\) and \(9\) are natural, and \(63\) is natural.
General idea:
For any natural numbers \(a\) and \(b\), the product \(a \times b\) is again a natural number.
Conclusion:
Natural numbers are closed under multiplication. So the given statement is false.
Note: Some books include \(0\) in natural numbers. Even then, \(0 \times 5 = 0\), which is still a natural (or whole) number in that definition.