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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a) If A∪B=A, then
b) If A∩B=A, then
c) If A−B=A, then
d) If A∩B=B∩A, then
A and B are any sets.
e) If A−B=B−A, then
or
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