Question

give an example of a relation which is symmetric and transitive but not reflexive​

Answer 1

Answer:

Relation R is not reflexive as (5, 5), (6, 6), (7, 7) ∉ R. Now, as (5, 6) ∈ R and also (6, 5) ∈ R, R is symmetric. ∴R is not transitive. Hence, relation R is symmetric but not reflexive or transitive.

Answer 2

Answer:

$\huge\boxed{\fcolorbox{black}{purple}{❥ ᴀɴsᴡᴇʀ}}$

ʀᴇʟᴀᴛɪᴏɴ ʀ ɪs ɴᴏᴛ ʀᴇғʟᴇxɪᴠᴇ ᴀs (5, 5), (6, 6), (7, 7) ∉ ʀ. ɴᴏᴡ, ᴀs (5, 6) ∈ ʀ ᴀɴᴅ ᴀʟsᴏ (6, 5) ∈ ʀ, ʀ ɪs sʏᴍᴍᴇᴛʀɪᴄ. ∴ʀ ɪs ɴᴏᴛ ᴛʀᴀɴsɪᴛɪᴠᴇ. ʜᴇɴᴄᴇ, ʀᴇʟᴀᴛɪᴏɴ ʀ ɪs sʏᴍᴍᴇᴛʀɪᴄ ʙᴜᴛ ɴᴏᴛ ʀᴇғʟᴇxɪᴠᴇ ᴏʀ ᴛʀᴀɴsɪᴛɪᴠᴇ.

ʜᴏᴘᴇ ɪᴛ ʜᴇʟᴘs ʏᴏᴜ! ❤

ᴛʜᴀɴᴋ ʏᴏᴜ ᴀɴᴅ ɢᴏᴏᴅ ʙʏᴇ!❤