Question

the formula A union B when A and B are finite serlt is​

Answer 1

Answer:

$What is the union of sets A and B?</p><p></p><p>The union of two sets A and B is the set of elements which are in A, in B, or in both A and B. In symbols, . As another example, the number 9 is not contained in the union of the set of prime numbers {2, 3, 5, 7, 11, ...} and the set of even numbers {2, 4, 6, 8, 10, ...}, because 9 is neither prime nor even.</p><p></p><p>}$

Answer 2

Cardinal Number of a set

The number of distinct elements or members in a finite set is known as the cardinal number of a set. Basically, through cardinality, we define the size of a set. The cardinal number of a set A is denoted as n(A), where A is any set and n(A) is the number of members in set A.

Consider a set A consisting of the prime numbers less than 10.

Set A ={2, 3, 5, 7}.

As the set A consists of 4 elements, therefore, the cardinal number of set A is given as n(A) = 4.

Properties related to difference, union and intersection and the cardinal number of set

i) Union of Disjoint Sets:

If A and B are two finite sets and if A ∩ B = ∅, then

n(A ∪ B) = n(A) + n(B)

In simple words if A and B are finite sets and these sets are disjoint then the cardinal number of Union of sets A and B is equal to the sum of the cardinal number of set A and set B.

Disjoint sets

Figure 1- Disjoint sets

The union of the disjoint sets A and B represented by the Venn diagram is given by A ∪ B and it can be seen that A ∩ B = ∅ because no element is common to both the sets.

ii) Union of two sets:

If A and B are two finite sets, then

n(A ∪ B) = n(A) + n(B) – n(A ∩ B)

Simply, the number of elements in the union of set A and B is equal to the sum of cardinal numbers of the sets A and B, minus that of their intersection.

Union of two sets

Figure 2- Union of two sets

In the figure given above the differently shaded regions depict the different disjoint sets i.e. A – B, B – A and A ∩ B