Set Theory Test Series Question

Question

Statement 1: If $A\subseteq B$ and $B \subseteq A$ then $A= B$

Statement 2: If $A= B$ then $A\subseteq B$ or $B \subseteq A$

Which of these statements are true?

Statement 1 is standard definition of Equivalence of 2 sets, so always true.

Statement 2 seems to be true but I am not sure.

Comments

@Aditya_ @Sunnidhya Roy Statement 2 would have been correct even if it was A=B -> A ⊆ B AND B⊆A too right?

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@Abhrajyoti00 yeah it should be true.

This kind of scenario can never arise where A=B but either of A ⊆ B or B  ⊆  A is false. Both of them will always be true if we are given that A=B.

And also, if the Statement 2 was what you have written, then Statement 1 and Statement 2 would have been converses to each other.

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Yes if we use venn diagrams, we can see that both the sets are same, i.e one circle. So both are subsets of each other.