Question

A interset A is equal to pie
proof that​

Answer 1

Answer:

Yes. The solution works, although I'd express the second last step slightly differently.

A∪∅A∩∅={x:x∈A∨x∈∅}={x:x∈A}=A={x:x∈A∧x∈∅}={}=∅definition of union¬∃x (x∈∅)definition of intersection¬∃x (x∈∅∧x∈A)

A∪∅=A because, as there are no elements in the empty set to include in the union therefore all the elements in A are all the elements in the union. Hence the union of any set with an empty set is the set.

A∩∅=∅ because, as there are no elements in the empty set, none of the elements in A are also in the empty set, so the intersection is empty. Hence the intersection of any set and an empty set is an empty set.

hope it's help u