ajay kumar maths set relationship and functions

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1. SET RELATIONSHIPS Done BY: Bharath Kumar Class: XI-A

2. UNIVERSAL SET It is a set contain all things that have relevance to the group. EX : Set A: {1, 2, 3} Set B: {3, 4, 5} Set C: {5, 6, 7} The universal set (U) for these sets would be:  U:  {1, 2, 3, 4, 5, 6, 7} .

3. VENN DIAGRAM A visual representation of sets and their relationships using overlapping circles or other closed curves. Venn diagrams are used to illustrate concepts like union, intersection, and complement of sets, making it easier to understand set theory and related topics.  Ex: Set,Subset,Union,Intersection.

4. EQUAL SETS Two sets, A and B, are equal if and only if every element of A is an element of B, and every element of B is an element of A. This can be written as: A = B if and only if (A ⊆ B) and (B ⊆ A).   Example: {1, 2, 3} and {3, 1, 2} are equal sets because they contain the same elements. 

5. SUBSETS Set A is said to be a subset of Set B if all the elements of Set A are also present in Set B.   Set A is contained inside Set B. Ex: Set A = {1, 2, 3} Set B = {1, 2, 3, 4, 5}. The Null set is always a subset of Any set.

6. OPERATIONS ON SETS

7. UNION It is a set containing all elements from the original sets, without repetition. Ex: A ∪ B ={1,2,3,4,5,6,7,8} C ∪ D ={6,7,8,9,10,11,12}

8. INTERSECTION  The intersection of two sets, A and B, is denoted as A ∩ B and contains all elements that are present in both set A and set B.  Example:  If set A ={1,2,3,4} and set B ={3,4,5,6}. Symbol: The symbol "∩” represents the intersection operation .

9. SET DIFFERENCE Set difference, denoted as A - B, is a set operation that results in a new set containing elements that are present in set A but not in set B. In essence, it's the process of removing elements of set B from set A. Example: If A = {1, 2, 3, 4} and B = {3, 4, 5, 6}, then A - B = {1, 2}.  

10. COMPLIMENT The complement of set A is defined as a set that contains the elements present in the universal set but not in set A. For example, Set U = {2, 4, 6, 8, 10, 12} and set A = {4, 6, 8}, then the complement of set A, A′ = {2, 10, 12}. Example: ‘A’