Hi i have been working on a question is R anti-symmetric, irreflexive? A ={1,2,3,4} R= {(1,3),(1,2),(3,2),(4,4)}
I worked out R is not anti- symmetric and is not irreflexive since (4,4) is related. The answer states i am wrong, can someone please help me understand this as other definitions have not help. Thank you in advance
A relation $R$ is anti symmetric iff $$ (aRb \text { & } bRa) \implies a=b$$
This is what we have with our $R$.
The only case of $$ (aRb \text { & } bRa)$$ is $4R4$ and we have $4=4$ which makes our relation anti-symmetric.