Question

what is commutative property​

Answer 1

Answer:

binary operation is commutative if changing the order of the operands does not change the result. It is a fundamental property of many binary operations, and many mathematical proofs depend on it.

Answer 2

♕︎ǫᴜᴇsᴛɪᴏɴ♕︎

ᴡʜᴀᴛ ɪs ᴄᴏᴍᴍᴜᴛᴀᴛɪᴠᴇ 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

♕︎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.