Question

If A and B are sets such that A contains B and A is closed. Does that mean that B is closed too? Thank you.

Answer 1

not necessarily

if two elements in set A are combined with some binary operation, they will definitely land back in A (since A is closed), but they may land in B or they may land outside of B

Answer 2

so if you start with two elements in B, combine them with a binary operation, the result may or may not be in set B (it will definitely remain in set A though)

Answer 3

@jim_thompson5910 this is my question.