'A' and 'B' are disjoint sets : What do you say about AOB?
Express in your own words.
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Answer:
Two sets are said to be disjoint if they have no element in common. Equivalently, disjoint sets are sets whose intersection is the empty set. For example, {1, 2, 3} and {4, 5, 6} are disjoint sets,( as they have no element in common) while {1, 2, 3} and {3, 4, 5} are not.(as the element 3 is in common).
The union of two sets A and B is the set of elements which are in A, in B, or in both A and B. In figures;
First consider the case where the sets A and B are disjoint.
In that case,
The number of elements in the union (A∪B) is simply the sum of the number of elements in A and the number of elements in B: |A ∪ B| = |A| + |B|. [ |A|→no of elements in A and other notations mean similar].
But if A and B overlap, then the latter formula does not hold because, we are counting the elements in the intersection (A ∩ B) twice. Compensating for that leads to the given formula: |A ∪ B| = |A| + |B| − |A ∩ B|.
[ Note : n(A U B) is also denoted as |A U B| ]
In figure of Disjoint sets;
Elements in (AUB)=elements in (A)+ elements in (B).
In above example, union of disjoint sets is;
Element set in A + Element set in B
={1,2,3,5,7,9}.
