Question

If A and B are two disjoint sets, then find the cardinal number of A uniun B​

Answer 1

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 above 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}.