A set is a well-defined collection of objects. Venn diagrams are pictorial representations of sets and their relationships. Sets and Venn diagrams are
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What is the difference between a subset and an element?
An element is a single object in a set (written a ∈ A). A subset is a set whose elements are all in another set (written A ⊆ B). Example: 2 ∈ {1, 2, 3} but {2} ⊆ {1, 2, 3}.
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Why is the formula for union |A ∪ B| = |A| + |B| - |A ∩ B|?
When counting |A| + |B|, elements in the intersection |A ∩ B| are counted twice. So we subtract |A ∩ B| once to avoid double-counting.
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Can two sets be equal and disjoint at the same time?
No, except for the empty set. Equal sets have the same elements, so their intersection is the entire set. Disjoint sets have no common elements. Only ∅ and ∅ satisfy both conditions.
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