The study of sets helps in increasing the degree of relations in such a way that it optimizes the bond
between any two ,three or many quantities taken together.
Set: A well-defined collection of objects is defined as a set.
Example: Set of vowels A= {a, e, i, o, u}
Note: All the sets are denoted by capital letters
Symbols used in sets:
Union: U
Intersection: ∩
Subset: C
If there are two sets given say A and B then the common data found in these two sets is called common data set.
Example A= {a, e, i, o, u} B= {a, i, o}
Then we find the common data set between these two sets namely A ∩ B = {a, i, o}.
The joining of two set elements together is called union of sets
Example: A= {2, 5, 7} B= {a, g, h}
AUB = {a, g, h, 2, 5, 7}
Example A= {1, 5} B= {5}
Then we find the common data set between these two sets namely A ∩ B = {5}.
What is a cardinal number? The number of elements in the given set is called a cardinal number.
Example: A= {1, 2, a, v}
In the above example there are 4 elements in the given set.
Hence we define cardinal number as 4.
Sets Solved Problems
Given A= {1, 2} B= {6, 3}
Find
1. A ∩ B
2. AUB
3. Cardinal number of A and B
If A= {2, 6, 7, 8} B= {2, 6, 3} find A ∩ B
A ∩ B = {2, 6}, so the common elements are shaded in yellow.
In a total of 30 players , 25 play hockey and 10 play Rugby can you predict using set theory that how players are liking to play both.
The formulae is n (A U B) = n (A) + n (B) - n (A ∩ B)
Here n (A U B) = cardinal number of both set A and set B (hockey and rugby)
n (A)= cardinal number of only set A (Hockey only)
n (B) = cardinal number of only set B (Rugby).
And
n (A ∩ B) = cardinal number for both hockey and rugby
30 = 25 +10 - n (A ∩ B) so transfer n (A ∩ B) towards left side we get
n (A ∩ B) = 35-30
= 5
So the number of players who play both is 5.
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