Question

What is difference between commutative and closure property
???

Answer 1

Step-by-step explanation:

CLOSURE PROPERTY OF ADDITION., a+b=c, eg 2+3=5.... MULTIPLICATION =a*b=c, eg =2*3=6... COMMUTATIVE PROPERTY OF ADDITION=a+b=b+a, eg, 2+3=3+2

Answer 2

♕︎ǫᴜᴇsᴛɪᴏɴ♕︎

ᴡʜᴀᴛ ɪs ᴅɪғғᴇʀᴇɴᴄᴇ ʙᴇᴛᴡᴇᴇɴ ᴄᴏᴍᴍᴜᴛᴀᴛɪᴠᴇ ᴀɴᴅ ᴄʟᴏsᴜʀᴇ ᴘʀᴏᴘᴇʀᴛʏ?

♕︎ᴀɴsᴡᴇʀ♕︎

ғᴏʀ ᴀᴅᴅɪᴛɪᴏɴ, ᴛʜᴇ ᴏʀᴅᴇʀ ᴏғ ᴛʜᴇ ɴᴜᴍʙᴇʀs ᴅᴏᴇs ɴᴏᴛ ᴍᴀᴛᴛᴇʀ. sᴏ, ᴇᴠᴇɴ ɪғ ʏᴏᴜ ʀᴇᴠᴇʀsᴇ ᴛʜᴇ ᴏʀᴅᴇʀ ᴏғ ᴛʜᴇ ɴᴜᴍʙᴇʀs ᴀɴᴅ ᴀᴅᴅ ᴛʜᴇᴍ, ᴛʜᴇ ᴇɴᴅ ʀᴇsᴜʟᴛ ʀᴇᴍᴀɪɴs ᴛʜᴇ sᴀᴍᴇ. ᴛʜɪs ᴘʀᴏᴘᴇʀᴛʏ,ᴡʜᴇʀᴇ ᴛʜᴇ ʀᴇsᴜʟᴛ ᴅᴏᴇs ɴᴏᴛ ᴅᴇᴘᴇɴᴅ ᴏɴ ᴛʜᴇ ᴏʀᴅᴇʀ ɪɴ ᴡʜɪᴄʜ ᴛʜᴇ ɴᴜᴍʙᴇʀs ᴀʀᴇ ᴛᴀᴋᴇɴ ғᴏʀ ᴀɴ ᴀʀɪᴛʜᴍᴇᴛɪᴄ ᴏᴘᴇʀᴀᴛɪᴏɴ, ɪs ᴄᴀʟʟᴇᴅ ᴄᴏᴍᴍᴜᴛᴀᴛɪᴠᴇ ᴘʀᴏᴘᴇʀᴛʏ.

ᴇxᴀᴍᴘʟᴇ:- 1 + 2 = 2 + 1

ᴛʜᴇ ᴄʟᴏsᴜʀᴇ ᴘʀᴏᴘᴇʀᴛʏ sᴛᴀᴛᴇs ᴛʜᴀᴛ ᴀ sᴇᴛ ᴏғ ɴᴜᴍʙᴇʀs (ᴇ.ɢ. ᴡʜᴏʟᴇ ɴᴜᴍʙᴇʀs) ɪs ᴄʟᴏsᴇᴅ ᴜɴᴅᴇʀ ᴀɴ ᴏᴘᴇʀᴀᴛɪᴏɴ ɪғ ᴛʜᴇ ʀᴇsᴜʟᴛ ᴏғ ᴛʜᴀᴛ ᴏᴘᴇʀᴀᴛɪᴏɴ ʙᴇᴛᴡᴇᴇɴ ᴀɴʏ ᴛᴡᴏ ɴᴜᴍʙᴇʀs ᴏғ ᴛʜᴇ sᴇᴛ ɪs ᴀʟsᴏ ᴀ ᴍᴇᴍʙᴇʀ ᴏғ sᴀᴍᴇ sᴇᴛ ( ɪɴ ᴛʜɪs ᴄᴀsᴇ ᴀ ᴡʜᴏʟᴇ ɴᴜᴍʙᴇʀ).

ᴛʜᴇ sᴇᴛ ᴏғ ᴡʜᴏʟᴇ ɴᴜᴍʙᴇʀs ɪs ᴄʟᴏsᴇᴅ ᴜɴᴅᴇʀ ᴀᴅᴅɪᴛɪᴏɴ ʙᴇᴄᴀᴜsᴇ ᴛʜᴇ ᴀᴅᴅɪᴛɪᴏɴ ᴏғ ᴛᴡᴏ ᴡʜᴏʟᴇ ɴᴜᴍʙᴇʀs ᴀʟᴡᴀʏs ʀᴇsᴜʟᴛs ɪɴ ᴀ ᴡʜᴏʟᴇ ɴᴜᴍʙᴇʀ.

ᴇxᴀᴍᴘʟᴇ :- 2 + 1 = 3

♕︎ᴀᴅᴅɪᴛɪᴏɴᴀʟ ɪɴғᴏʀᴍᴀᴛɪᴏɴ♕︎

• ᴛʜᴇ ᴄᴏᴍᴍᴜᴛᴀᴛɪᴠᴇ ᴘʀᴏᴘᴇʀᴛʏ ᴏғ ᴀᴅᴅɪᴛɪᴏɴ ғᴏʀ ʀᴀᴛɪᴏɴᴀʟ ɴᴜᴍʙᴇʀs sᴛᴀᴛᴇs ᴛʜᴀᴛ ғᴏʀ ᴀɴʏ ᴛᴡᴏ ʀᴀᴛɪᴏɴᴀʟ ɴᴜᴍʙᴇʀs, ᴀ/ʙ ᴀɴᴅ ᴄ/ᴅ, ᴀ/ʙ + ᴄ/ᴅ = ᴄ/ᴅ + ᴀ/ʙ
• ғᴏʀ sᴜʙᴛʀᴀᴄᴛɪᴏɴ ʜᴏᴡᴇᴠᴇʀ, ᴏʀᴅᴇʀ ᴏғ ᴛʜᴇ ɴᴜᴍʙᴇʀs ᴍᴀᴛᴛᴇʀ. ᴄʜᴀɴɢɪɴɢ ᴛʜᴇ ᴏʀᴅᴇʀ ɢɪᴠᴇs ᴀ ᴅɪғғᴇʀᴇɴᴛ ᴀɴsᴡᴇʀ. ᴛʜᴀᴛ's ᴡʜʏ ᴜɴᴅᴇʀ sᴜʙᴛʀᴀᴄᴛɪᴏɴ, ᴛʜᴇ ʀᴀᴛɪᴏɴᴀʟ ɴᴜᴍʙᴇʀs ᴀʀᴇ ɴᴏᴛ ᴄᴏᴍᴍᴜᴛᴀᴛɪᴠᴇ.
• sᴏ, ғᴏʀ ᴀɴʏ ᴛᴡᴏ ᴅɪsᴛɪɴᴄᴛ ʀᴀᴛɪᴏɴᴀʟ ɴᴜᴍʙᴇʀs ᴀ/ʙ ᴀɴᴅ ᴄ/ᴅ, ᴀ/ʙ - ᴄ/ᴅ = ᴄ/ᴅ - ᴀ/ʙ
• ʀᴀᴛɪᴏɴᴀʟ ɴᴜᴍʙᴇʀs sᴀᴛɪsғʏ ᴄᴏᴍᴍᴜᴛᴀᴛɪᴠᴇ ᴘʀᴏᴘᴇʀᴛʏ ᴜɴᴅᴇʀ ᴀᴅᴅɪᴛɪᴏɴ ᴀɴᴅ ᴍᴜʟᴛɪᴘʟɪᴄᴀᴛɪᴏɴ.
• ғᴀᴄᴛ :- ᴛʜᴇ ᴡᴏʀᴅ "ʀᴀᴛɪᴏɴᴀʟ" ʜᴀs ɪᴛs ʀᴏᴏᴛs ɪɴ ᴛʜᴇ ᴡᴏʀᴅ "ʀᴀᴛɪᴏ" ɪɴ ᴍᴀᴛʜᴇᴍᴀᴛɪᴄs. ᴇᴠᴇʀʏ ʀᴀᴛɪᴏɴᴀʟ ɴᴜᴍʙᴇʀ ɪs ᴀᴄᴛᴜᴀʟʟʏ ᴊᴜsᴛ ᴀ ʀᴀᴛɪᴏ ᴏғ ᴛᴡᴏ ɪɴᴛᴇɢᴇʀs.
• ɴᴏɴᴇ ᴏғ ᴡʜᴏʟᴇ ɴᴜᴍʙᴇʀs, ɪɴᴛᴇɢᴇʀs ᴏʀ ʀᴀᴛɪᴏɴᴀʟ ɴᴜᴍʙᴇʀs ғᴏʟʟᴏᴡ ᴄʟᴏsᴜʀᴇ ᴘʀᴏᴘᴇʀᴛʏ ᴜɴᴅᴇʀ ᴅɪᴠɪsɪᴏɴ.
• ɪɴᴛᴇɢᴇʀs ᴀɴᴅ ʀᴀᴛɪᴏɴᴀʟ ɴᴜᴍʙᴇʀs ᴀʟsᴏ ғᴏʟʟᴏᴡ ᴄʟᴏsᴜʀᴇ ᴘʀᴏᴘᴇʀᴛʏ ᴜɴᴅᴇʀ sᴜʙᴛʀᴀᴄᴛɪᴏɴ.
• ᴡʜᴏʟᴇ ɴᴜᴍʙᴇʀs, ɪɴᴛᴇɢᴇʀs, ᴀɴᴅ ʀᴀᴛɪᴏɴᴀʟ ɴᴜᴍʙᴇʀs ғᴏʟʟᴏᴡ ᴄʟᴏsᴜʀᴇ ᴘʀᴏᴘᴇʀᴛʏ ᴜɴᴅᴇʀ ᴀᴅᴅɪᴛɪᴏɴ ᴀɴᴅ ᴍᴜʟᴛɪᴘʟɪᴄᴀᴛɪᴏɴ.