Sets of Functions

Question

Please provide feedback to my answer to this question. Question: For all sets A,B,C if A contain in B, B contain in C and C contain in A , then A=B=C. Answer: True, since; If we let x be element of A, since A contain in B, it implies that x is also an element of B, then A=B. If we let x be element of B, since B contain in C, it implies that x is also an element of C, then B=C. If we let x be element of C, since C contain in A, it implies that x is also an element of A, then C=A. Thus A=B=C.

Answer 1

Your answer is correct but the logic can be made more clear. Given that $A\subset B\subset C\subset A$ So $x\in A\Rightarrow x\in B$ as $A\subset B$ Similarly $x\in B\Rightarrow x\in A$ as $B\subset A$Thus $A=B$

Same argument will also work to prove $A=C$ since $A\subset C\subset A$

Thus $A=B=C$