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Union of Events

A fundamental operation through which sets are combined and related to each other. The term union tells us it is a collection of sets containing distinct elements. It is denoted by $\cup$. Combining the members of each we can find the union of any number of sets. For two sets A and B it is pronounced as A union B and is denoted as A $\cup$ B, In A $\cup$ B the set contains elements  that belong to either A or to B or to both. Union of sets will take everything that is in either of the sets. Remember that element is written only once even if they exist in both the sets.

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Definition

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Union of events definition:- Union of events is simply a union of two or more than two events. If two sets representing events are combined then we form a single set representing another event that contains all the events in a single set then it is said to be a union of events. The union of events or sets is denoted by sign U. If A and B are two events then A U B is called union of A and B.
suppose that two events are given A and B then 
The union of two events A and B is the event which consists all the elements of A and B.                     
 A = {a, b, c} and B = {x, y, z}
then                                 A U B = {a, b, c, x, y, z}

The venn diagram is as following:


There is an another example   A={0, a, b, c, 1, 2} and , B={1, 2}
                              A U B={0, 1, 2, a, b, c,} 

How to Calculate 

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The calculation of Union of events is easy to understand. If we have two sets of event and we are asked to find the union then we 
just collect all the elements of both given sets and put these in a new set and this new formed set is called union of events.
Like We have two sets of events A={1, 2, 3} and B={4, 6} these events are combined then we get A U B = {1, 2, 3, 4, 6}
Another Example: P = { x, y, z} and Q = {x, a, b} then P U Q = {x, y, z, a, b}
Note:- In above example we have x in both P and Q events but P U Q doesn't have two x because we know any element doesn't repeat itself in set.

Examples

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Example 1: If P={A, B, C} and Q = {1, 2, 3} then find out union of P and Q. 
 
Solution: - Given sets or events P={A, B, C} and Q={1, 2, 3}
                                                  
            So, 
                          P U Q= {1, 2, 3, A, B, C}                                       
                                                         
 Example 2: If P={x, y}, Q={a, b, c,} and R = {1, 2}}then find out P U Q U R.                                                    

 Solution:   
Given sets or events are 
                             P={x, y}, Q={a, b, c,} and R = {1, 2}
              So,
    
                            P U Q= {x, y, a, b, c, 1, 2}
Example 3: If A = { All positive numbers} and B = { All negative numbers} then find out A U B.
  Solution:-   Given events 
                                     A = { All positive numbers} and B = { All negative numbers}
                    Then A U B = {All integers}
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