Thanks for watching and good question! Recall what an antisymmetric relation is. If R is an antisymmetric relation, and a and b are distinct, then it must be that if aRb, it doesn't hold that bRa. In other words, if aRb and bRa, it must be that a = b. Distinct elements cannot relate in both directions if a relation is antisymmetric. So, for sets A and B, if A is a subset of B and B is a subset of A, does that imply that A = B? If so, subset is an anti-symmetric relation. So what do you think?
Thank you!
also "set" of all sets is not a set so can't have ANY relation on it.
me being Bertrand Russell nitpicky.
sir does power set relation is equivalence relation?
U r amazing
Thanks a lot for watching and for your support, Lavern! Let me know if you ever have any video requests!
Prove that the relation `R={(x,y): x, y in N and x-y \" is divisible by 7 \"}` defined on
Are you talking modulo relative to set theory?
Is the subset relation anti symmetric?
Thanks for watching and good question! Recall what an antisymmetric relation is. If R is an antisymmetric relation, and a and b are distinct, then it must be that if aRb, it doesn't hold that bRa. In other words, if aRb and bRa, it must be that a = b. Distinct elements cannot relate in both directions if a relation is antisymmetric.
So, for sets A and B, if A is a subset of B and B is a subset of A, does that imply that A = B? If so, subset is an anti-symmetric relation. So what do you think?