Subtraction is taking out a couple of items from several of those. For example: let us say you have basket with 7
apples and you take out 2 apples from it. Now, how many apples are left in the basket? The answer would be when
you substract the quantity that you are taking out (i.e., 2) from the quantity that was there (i.e., 7). So the
answer is: 7 - 2 = 5. You are left with 5 apples in the basket.
Note: We will subtract the smaller number from the larger number.
Select first number:
Select second number:
What you are seeing below is as many sticks as the larger of the two numbers:
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:
Equal Sets
If superset and subset have same number of elements, such that the two sets are fully overlapping each other then we call them 'Equal Sets'.
