For any sets A and B, A union B = A if and only if B subsetoforequalto A. For an

Question

For any sets A and B, A union B = A if and only if B subsetoforequalto A. For any sets A, B and C, A union (B intersection C) = (A union B) intersection (A union C). For any sets A and B, A union B wholebar = A bar intersection B bar. For any set A, A subsetoforequalto A. For any sets A and B, A intersection B subsetoforequalto A and A intersection B subsetoforequalto B. There exists a set A such that A subsetoforequalto A bar. For any set A, theta subsetoforequalto A. There exists a set B, such that B subsetoforequalto theta. For any set A, {theta} subsetoforequalto A. For any set A, A union A bar = U.

Explanation / Answer

We know that the empty set is a set with no elements.

Also, an empty set is is a subset of every set, including itself

i.e., A:A, (for any set A, is a subset of A)

including if A=: ==>

which means, B can be a subset of the empty set

if and only if; B is equal to the empty set:

BB=

Thus, there exists a set B, such that B

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