so i was reviewing topology and i came across some questions that i was not able to prove:

1)show that for a set E in R^n, the boundary of E is contained in the closure of E.

the given definition is that x is a boundary point of E if x is in the complement of int(E) U int(complement of E), and that the closure of E is the intersection of all closed sets containing E. i tried picking an x in the boundary of E, but couldnt relate it to the closure in anyway through set theoretic methods.

2) show that for a set E in R^n, closure of E = E U (the boundary of E).

again i know that the way to do it is set inclusion, but still have trouble relating the boundary of E to the closure of E.

thanks!