If then which of the following is not true?

Given: A ⊂ B means every element of A is also an element of B.

Consequences that follow from A ⊂ B:

• A ∪ B = B — since all elements of A are already in B, the union does not add anything new.

• A ∩ B = A — the intersection selects elements common to both sets, which are exactly the elements of A.

• Bᶜ ⊂ Aᶜ — taking complements reverses the inclusion relation: elements not in B are also not in A.

Why the statement "B − A = ∅" is not necessarily true:

The set difference B − A contains elements of B that are not in A. This will be empty only when B has no elements outside A, i.e., only when A = B.

Counterexample: Let A = {1} and B = {1, 2}. Then A ⊂ B, but B − A = {2} ≠ ∅. Hence the statement that B − A = ∅ does not follow from A ⊂ B in general.

Answer: The statement 'B − A = ∅' is not true in general.