Friday, 7 April 2023
Thursday, 6 April 2023
Lesson 1 - Introduction to Sets (And visualization using Venn Diagrams)
What are sets?
Definition 1 (from NCERT) A set is a well-defined collection of objects. The following points may be noted : (i) Objects, elements and members of a set are synonymous terms. (ii) Sets are usually denoted by capital letters A, B, C, X, Y, Z, etc. (iii) The elements of a set are represented by small letters a, b, c, x, y, z, etc. Some examples of sets: (i) Odd natural numbers less than 10, i.e., 1, 3, 5, 7, 9 (ii) The rivers of India (iii) The vowels in the English alphabet, namely, a, e, i, o, u (iv) Various kinds of triangles (v) Prime factors of 210, namely, 2,3,5 and 7 (vi) The solution of the equation: x2 – 5x + 6 = 0, viz, 2 and 3. We give below a few more examples of sets used particularly in mathematics, viz. N : the set of all natural numbers Z : the set of all integers Q : the set of all rational numbers R : the set of real numbers Z+ : the set of positive integers Q + : the set of positive rational numbers, and R + : the set of positive real numbers. Definition 2 Sets: grouping of elements and each element in the group is unique.Two basic types of sets: Overlapping sets and Non-overlapping sets.
Overlapping Sets
If there is one or more element present in both sets, the sets are called to be overlapping.Example of Overlapping Sets
Set1: First six natural numbers. Set2: First three natural numbers and first three alphabets. Now two sets together in a Venn Diagram.
set1 - set2 | Intersection | set2 - set1 |
Set1 Size: Diff Size: |
Intersection Size: |
Set2 Size: Diff Size: |
Example of Non-Overlapping Sets
Non-overlapping sets are better known as Disjoint Sets.
Set1: First six natural numbers. Set2: First six alphabets. Now two sets together in a Venn Diagram.
set1 - set2 | Intersection | set2 - set1 |
Set1 Size: Diff Size: |
Intersection Size: |
Set2 Size: Diff Size: |
Nomenclature for sets that are 'Overlapping'
Subset and Superset Relation
If each element of set A is in set B, and also we have some extra elements present in set B which are not in set A: Then, we call set A a subset and set B a superset. A superset has more number of elements than a subset. Set1: Letters from the word 'Rhythm'. Set2: English Consonants. Now two sets together in a Venn Diagram.
set1 - set2 | Intersection | set2 - set1 |
Set1 Size: Diff Size: |
Intersection Size: |
Set2 Size: Diff Size: |