If A is a proper subset of B can B be a proper subset of A?

Answer 1

Barring any sneaky tricks with the empty set, the answer is no.

Given: A is a proper subset of B.

Suppose B is a proper subset of A.

Since A is a proper subset of B, the every element of A is also in B AND

B contains at least one element that is not in A.

By supposition, sine B is a proper subset of A, every element of B

is also an element of A, which contradicts the previous statement.