Question

explain closure property of natural numbers​

Answer 1

Addition: When two natural numbers or whole numbers are added, the result is always a natural number or a whole number. For example, take any two natural numbers, say 3 and 9. Now, 3 + 9 = 12. 12 is a natural/whole number. Therefore, the system is closed under addition.

2) Subtraction: Subtraction of two whole or natural numbers does not always result in a whole number or natural number. For example, take any two natural numbers, say 3 and 9. Now, 3 – 9 = -6. -6 is not a natural/whole number. Therefore, the system is not closed under addition.

3) Multiplication: Multiplication of two whole or natural numbers always results in a whole or natural number. For example, 3 × 9 = 27, 27 is the natural number. Therefore, the system is closed under multiplication.

4) Division: Division of two whole or natural numbers does not always result in whole or natural numbers. For example, 3 ÷ 9 =

1

3

.

1

3

is not a natural number. Therefore, the system is not closed under division.

Answer 2

Answer:

(ɪ) ᴄʟᴏsᴜʀᴇ ᴘʀᴏᴘᴇʀᴛʏ : ᴛʜᴇ sᴜᴍ ᴏғ ᴀɴʏ ᴛᴡᴏ ɴᴀᴛᴜʀᴀʟ ɴᴜᴍʙᴇʀs ɪs ᴀʟᴡᴀʏs ᴀ ɴᴀᴛᴜʀᴀʟ ɴᴜᴍʙᴇʀ. ᴛʜɪs ɪs ᴄᴀʟʟᴇᴅ 'ᴄʟᴏsᴜʀᴇ ᴘʀᴏᴘᴇʀᴛʏ ᴏғ ᴀᴅᴅɪᴛɪᴏɴ' ᴏғ ɴᴀᴛᴜʀᴀʟ ɴᴜᴍʙᴇʀs. ᴛʜᴜs, ɴ ɪs ᴄʟᴏsᴇᴅ ᴜɴᴅᴇʀ ᴀᴅᴅɪᴛɪᴏɴ. ɪғ ᴀ ᴀɴᴅ ʙ ᴀʀᴇ ᴀɴʏ ᴛᴡᴏ ɴᴀᴛᴜʀᴀʟ ɴᴜᴍʙᴇʀs, ᴛʜᴇɴ (ᴀ + ʙ) ɪs ᴀʟsᴏ ᴀ ɴᴀᴛᴜʀᴀʟ ɴᴜᴍʙᴇʀ.

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