Question
Give an example of a universal set $U$, two sets $A$ and $B$ and accompanying Venn diagram such that $|A \cap B|=|A-B|=|B-A|=|\overline{A \cup B}|=2$.
Step 1
To satisfy the conditions given, we need to ensure that the universal set \( U \) contains enough elements to accommodate all the specified subsets and their intersections. Let's define \( U = \{1, 2, 3, 4, 5, 6, 7, 8\} \). Show more…
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Give an example of a universal set U and sets A, B, and C such that each of the following sets contains exactly one element: A ∩ B ∩ C, (A ∩ B) - C, (A ∩ C) - B, (B ∩ C) - A, A - (B ∪ C), B - (A ∪ C), C - (A ∪ B), A ∪ B ∪ C. Draw the accompanying Venn diagram.
1.23. Give examples of two sets A and B such that |A - B| = |A ∩ B| = |B - A| = 3. Draw the accompanying Venn diagram. 1.25. Give examples of three sets A, B, and C such that B ∈ A, B ⊂ C, and A ∩ C = ∅. 1.27. Give an example of a universal set U, two sets A and B, and an accompanying Venn diagram such that |A ∩ B| = |A - B| = |B - A| = |A ∪ B| = 2.
Suppose A and B are sets. Give a Venn diagram to represent (A - B) ∪ (B - A) ∪ (A ∩ B) and using the same, find a simple expression.
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