How to determine whether two sets are equal?

Questions
1

Based on the comments here and here, I find the following method to determine whether two sets are equal:

a = {1, 2, 3};
b = {1, 3, 2};
If[AllTrue[a, MemberQ[b, #] &] && AllTrue[b, MemberQ[a, #] &], 
 Print["a=b"], Print["a\[NotEqual]b"]]

a=b

But this method seems quite cumbersome. Are there any good suggestions?

Regards,
HZ

2

Maybe Sort[a]===Sort[b].

3

Yes, they all work:

a = {1, 2, 3};
b = {1, 3, 2};
If[AllTrue[a, MemberQ[b, #] &] && AllTrue[b, MemberQ[a, #] &], 
 Print["a=b"], Print["a\[NotEqual]b"]]
If[Sort[a] === Sort[b], Print["a=b"], Print["a\[NotEqual]b"]]

a=b

a=b

But, can we always ensure that these methods are absolutely equivalent?

4

That would depend on internals of MemberQ in terms of how it determines equivalence. But you’ve posed a question that, as it stands, is not possible to answer. You have neglected to provide any details about the types of sets you will consider for such testing. Are they always symbols? Exact numbers? Real numbers, possibly with different precisions? Perhaps more importantly, do you consider multiplicitiy of elements as meaningful? If not, then Sort won’t be the function to use, since for example {a,a,b}=!={a,b}.

5

Thank you for your systematic, insightful and in-depth comments. I will supplement and explain in the future according to the actual situation.

6

Union[a, b] == Intersection[a, b]