Is Subset an Equivalence Relation? | Set Theory

[@keldonchase4492]

Thank you!

[@benshapiro8506]

also "set" of all sets is not a set so can't have ANY relation on it.
me being Bertrand Russell nitpicky.

[@combinedmathsbysachithband5680]

sir does power set relation is equivalence relation?

[@itsev6970]

U r amazing

[@WrathofMath]

Thanks a lot for watching and for your support, Lavern! Let me know if you ever have any video requests!

[@TurningTablesforyou]

Prove that the relation `R={(x,y): x, y in N and x-y \" is divisible by 7 \"}` defined on

[@vonBottorff]

Are you talking modulo relative to set theory?

[@deepakpriyadharshan]

Is the subset relation anti symmetric?

[@WrathofMath]

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?