One of the main applications of Sets theory is to make the Relations between two sets. For making these relations, certain operations can be performed on the Numbers. We will discuss Some Basic Operations on Sets.
Union: As the word indicates Union means joining or adding together. Union of Two sets means adding together the two sets. Let us consider two sets ‘A’ and ‘B’, then the union of two sets is represented by “A U B”, which means all the elements which either belong to ‘A’ or ‘B’. Here are some examples: If A= 1, 2, 3 and B= Red, Blue
So we have A U B = 1, 2, Red, Blue
Again if A = 1, 3, 5 and B = 2, 3, 4, 6.
So we have A U B = 1, 3, 5, 2, 4, 6.
Also if A= 1, 2 and B = 1, 2.
So we have A U B = 1, 2.
Following are some properties of Union of sets:
a) A U B = B U A, this property is known as Commutative Property.
b) A U ( B U C ) = ( A U B ) U C, this property is known as Associative Property.
c) A U A = A,
d) A U φ = A,
e) ‘A’ is the subset of ‘B’ if A U B = B.
Intersection: We can also form a new Set by determining the common elements of the given two sets. This is called Intersection of the two sets.
The intersection of 'A' and 'B', denoted by A B
If A B =φ , then 'A' and 'B' are called disjoint sets.
Set can be defined as the collection of well defined and distinct objects, considered as an object. While studying Sets theory, we need to reform the group of the sets in order to get the solutions. One of the main applications of the sets theory is to make the Relations between two sets. For making these relations, certain operations can be performed on the Numbers. We will discu...Read More
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We can say that a Set is the collection of different objects grouped together. Any set is the most basic element used in mathematics. In everyday life we observe that Sets are used to make groups of same type of elements. When we study sets theory, we need to re- organize the group of the sets which always helps us to get the solutions. One of the main applications of the s...Read More