A subset is a set that contains some or all of the elements of another set. For example, if we have Set A = {1, 2, 3} and Set B = {3, 2, 1}, then A is a subset of B, because all the elements of Set A are also elements of Set B. We represent this using the subset symbol, A ⊆ B.
A proper subset is a subset that contains some but not all of the elements of another set. For example, if we have Set C = {1, 2, 3, 4} and Set D = {1, 2, 3}, then D is a proper subset of C, because D contains some but not all of the elements of C. We represent this using the proper subset symbol, D ⊂ C.
A proper subset is a subset that contains some but not all of the elements of another set. However, in the case of Sets A and B, since they are equal (i.e., A = B), neither one is a proper subset of the other.
It's important to note that if we reverse the sign of the subset symbol, we get the superset symbol. So, if Set C is a superset of Set D, we write C ⊇ D, which means that C contains all the elements of D.
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