# Proper and Improper Subset – 9th and 10 Maths

## Proper and Improper Subset – 9th and 10 Maths

In Today’s Student Tube lecture we will discuss about Proper and Improper Subsets from Exercise 1.1 – Chapter 1 (9 & 10 Mathematics – Sindh Board Education)

### What is Subset?

A set A is a subset of another set B if all of its elements are also members of the set B. In other words, set A is found within set B. The subset relationship is denoted by symbol  A⊂B.

Example of Subset:

For example, if set A has {1,2} and set B has {1,2,3,} then A is a subset of B since elements of set A are present in set B.

### What is a Proper subset?

A is a proper subset of B if and only if, every element of A in B, but there is at least one element of B that is not in A.

### What is Improper subset?

Improper subset is a subset containing every elements of the other set.

Example of Proper subset:

A = { 1, 3, 5 } And B = {1, 2 3, 5,}

A set is “A” subset of “B” because all the elements of set “A” are in “B” but there is an element 2 of B which is not in A.

Example of Improper subset:

Let A = { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10}

Subsets of the Set A are:

B= { 1, 2, 3, 4}

C= { 6, 7, 8, 9}

D = { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10}

now, B and C sets are proper subsets while set D contains all the elements of the original set.

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