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Suppose we have two sets A & B, then A < B is:True if len(A) is less than len(B).True if A is a proper subset of B.True if the elements in A when compared are less than the elements in B.True if A is a proper superset of B.

Question

Suppose we have two sets A & B, then A < B is:True if len(A) is less than len(B).True if A is a proper subset of B.True if the elements in A when compared are less than the elements in B.True if A is a proper superset of B.

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Solution

The statement "A < B" can be interpreted in different ways depending on the context. Here are the interpretations based on your statements:

  1. True if len(A) is less than len(B): This is true in the context of comparing the sizes of the sets. If the number of elements in set A is less than the number of elements in set B, then we can say "A < B".

  2. True if A is a proper subset of B: This is true in the context of set theory. A proper subset is a subset that is not equal to the set itself. So, if all elements of A are in B but B contains at least one element not in A, then A is a proper subset of B.

  3. True if the elements in A when compared are less than the elements in B: This could be true in a context where the elements of the sets are numbers and each element in A is less than each element in B. However, this is not a standard interpretation of "A < B" in set theory.

  4. True if A is a proper superset of B: This is not true. If A is a proper superset of B, it means that A contains all elements of B and at least one additional element. In this case, we would say "A > B", not "A < B".

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