Question:

We know that Natural Numbers are closed under addition (the sum of any two natural numbers is always a natural number). Are they closed under subtraction? Provide a couple of examples to justify your answer.
[Page No. 43]

Answer: Verified

No, Natural numbers are not closed under subtraction.
Example 1: 5 - 3 = 2 (natural number)
Example 2: 3 - 5 = -2 (not a natural number)
Example 3: 4 - 4 = 0 (not a natural number, since N = {1, 2, 3, ...})
Since we can find two natural numbers whose difference is not a natural number, the set N is not closed under subtraction.

Concept Applied
Natural numbers are closed under addition and multiplication, but not under subtraction or division, which is why the number system is extended to integers and rational.

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We know that Natural Numbers are closed under addition (the sum of any two natural numbers is always a natural number). Are they closed under subtraction? Provide a couple of examples to justify your answer. [Page No. 43]

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We know that Natural Numbers are closed under addition (the sum of any two natural numbers is always a natural number). Are they closed under subtraction? Provide a couple of examples to justify your answer.
[Page No. 43]