sets-3rd-class 10-mathematics-English medium-subset-proper subset-super set-universal set-equal sets

 Sets-class.10-mathematics

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1.Subset & Super set:

Let A and B are two Non-empty sets.
If Every element of set A is a member of Set B, then set A is called subset of Set B.

we write as A⊆B
read as "A is subset of B"

And set B is called Super set of set A

we denotes B⊃A
read as "B is super set of A"

NOTE:

Sets A and B are EQUAL SETS,
If and only if every element of set A is a member of set B
and every element of set B  is a member of set A.

"If A⊆B and B⊆A then A and B are called Equal sets"

"If A=B then A⊆B and B⊆A"

NOTE:

Null set(∅) is subset to every set

And

Every set is subset to itself

Suppose A={3, 4, 5, 7 } and ∅={   }

∅ has no elements
So,  ∅ is subset to A

And every element of set A is member of set A
So, A is subset to A(itself)

Example.1:

A={1, 2, 3, 4} and B={2, 4}

Every element of set B is the element of set A
So
set B is subset of set A
∴ B⊂A

And
set A is called Super set of set B
∴ A⊃B

Example.2:

P is the set of factors of 5
Q is the set of factors of 25

first we know the elements of sets
P={1, 5}
Q={1, 5, 25}

Here Every element of set P is the element of set Q
So
set P is subset of set Q
∴ P⊂Q
And

set Q is called Super set of set P
∴ Q⊃P

Example.3:

X={x/x is a letter of the word "WOLF"}
Y={x/x is a letter of the word "FOLLOW"}

first we know the elements of sets
X={ w, o, l, f }
Y={f, o, l, w}

Here Every element of set X is the element of set Y
So
set X is subset of set Y
∴ X⊂Y

And
Every element of set Y is the element of set X
So
∴ Y⊂X

Here X⊂Y and Y⊂X
So, X, Y are equal sets
∴ X=Y

2.Proper subset:

If every element of set A is a member of set B and atleast one element of set B is not a member of set A then "set A is proper subset of set B"

In other words
If every element of set A is presents in set B but set A is not equal set to set B then set A is called proper subset of set B.

Let A⊂B and A≠B, 
∴ A is proper subset of B

3.Universal set:

A set super set of all sets of under our consideration is called "Universal set"

It is denoted by "U" or "μ"

Here all the sets under our consideration are the subsets to Universal set

For example,

We take all classes in our school as sets

Then

School set is Universal set

Because all class sets are subsets to School set

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similarly

In a village,

Let's take male people are one set and 

female people are other set

 Then the set of village people is universal set

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similarly, 

Prime Numbers and Composite Numbers are belongs to Natural numbers

And,

Natural number set is a super set for Prime Number set and Composite Numbers set 

So,

Set of Natural numbers is Universal set

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