Discrete math, antisymmetric proof question
Show that if R is an antisymmetric relation on S then any relation is also antisymmetric. I think how you solve it is if (x,y) are in R, they must be in R' since R' is a subset of R, thus (x,y) are in R'. To be antisymmetric x has to be related to y and y has to be related to x such that . And since R is antisymmetric and x,y are in R and R' is a subset then x,y in R' follow the same condition of R making them antisymmetric. That's one way I think it's solved but not 100% sure.