In this page,
we are going to know the "Operations on sets"
There are Three Basic operations. Those are Union of sets, intersection of sets and difference of sets.
Before going to know the operations on sets
first we know the Introduction of sets and Types of sets
Now let us learn about,
Let A and B are two Non-empty sets
"A set with elements from set A and Set B is called Union set of set A and set B"
we denote Union set of A and set B as "A∪B".
we read as "A union B"
The element of A∪B is an element of either set A or set B or Both.
A∪B is represents in Set builder form as follows
A∪B={x : x 𝞊 A or x 𝞊 B }
Example-1.
A={1, 2, 3, 4 } and B={2, 4, 6, 8, 9 }
All the elements from two sets, write in one set
(keep in mind, No element can repeat in a set)
∴ A∪B={1, 2, 3, 4, 6, 8, 9 }
Example-2.
P={a, e, i, o, u } and Q={a, b, c, d, e }
All the elements from two sets, write in one set
∴ P∪Q={a, e, i, o, u, b, c, d }
(write all elements from first set then write elements from second set. If any element member in two sets , write only one time)
Example-3.
A={2, 3, 5, 7 } and Ø ={ }
All the elements from two sets, write in one set
A∪Ø={2, 3, 5, 7 }
∴ A∪Ø=A
(write all elements from first set then write elements from second set. But here no element in second set because it is Null set. So we get first set as answer )
Example-4.
A={4, 6, 8, 9, 10 } and A={4, 6, 8, 9, 10 }
write all elements from first set then write elements from second set.
A∪A={4, 6, 8, 9, 10 }
∴ A∪A=A
(All the elements in two sets are same and no element repeats. So we got answer as first set)
Note:
1. AUB = BUA
2. AUØ = ØUA = A
3. AUA = A
4. AUB is super set to set A and set B
5. set A is subset to AUB. (A ⊂ AUB)
6. set B is subset to AUB. (B ⊂ AUB)
7. If A ⊂ B, then AUB = BUA = B
7. If B ⊂ A, then AUB = BUA = A