Solution to Given two sets A and B, for each of the following statements, what can you … - Sikademy
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Archangel Macsika

Given two sets A and B, for each of the following statements, what can you conclude about the sets? For example: consider the statement A−B=∅, this could be possible if - Scenario - 1: if A=B then A−B=∅ Scenario - 2: Since A−B=A−(A∩B), if (A∩B) = A then A−B=∅ Scenario - 3: A=∅ in which case, no matter what B is A−B=∅. Therefore we can conclude that if A−B=∅, then one of the above scenarios must be true. You do not need to draw exactly 3 conclusions. Try to answer with an exhaustive list of conclusions you can draw from each of the following statements: (a) A∪B=A (b) A∩B=A (c) A−B=A (d) A∩B=B∩A (e)A−B=B−A

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Here's the Solution to this Question

a) If A∪B=A, then

B\subseteq A


b) If A∩B=A, then

A\subseteq B


c) If A−B=A, then

B=\empty


d) If A∩B=B∩A, then

A and B are any sets.


e) If A−B=B−A, then

A=B

or

A=\empty

or

B=\empty

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