If A intersection B' is null set prove that A is subset of B

Question

About sets identities and proof of sets

Answer 1

To show that the set A is a subset of the set B we need to start with an element x of A and show that x belongs to the set B too. Indeed, since A intersection B'= empty set it means that no element of A belongs to the complement of the set B. Hence, all elements of A belong to set B or in other words, A is a subset of B which concludes the proof.