Question

Proper subset Explanation with some examples.
Please explain fast.​

Answer 1

SUBSET:

• The subset is a part of set whose all element are present in a lerger set.

• Symbol of subset is ⊂.

•°• Consider a set A = { x : x is a natural number}

•°• Consider a set B = { 1, 2, 3, 4, 5}

•°• Cosider a set C = {-1 , -2, 0, 11, 12, 13 }

• All the elements are B are natural numbers.

•°• So B ⊆ A .

• But in case of set C { - 1, -2, 0} along with some natural numbers are present. - 1, -2 ,0 are integers also 0 ∈ W and ∉ ℕ

•°• So C is here a improper subset.

ADDITIONAL POINTS:

• Empty set is a subset of all sets.

• For every set that set itself considered as a subset.

• Proper subset is a type of subset in which all elements of a smaller set are present in larger set without leaving atleast one element.

• Symbol of proper subset is ⊆.

NOTE : REFER ATTACHMENT FOR SET DIAGRAM.

Answer 2

Answer:

Subset:

If A and B are two sets and every element of A is an element of B, then A is the subset of B

Proper Subset:

→A subset is called a proper subset when all the elements of B are not in A, that is A ≠ B, but all elements of A is in B. Then it is written in the form A⊂ B.

→A proper subset contains some but not  every element of the original set.

→ The empty set is a proper subset of the original subset.

Some examples:

1. Let A = { 1, 2, 3, 4}. Let B = {2, 3}

Here B is a proper subset of A since B contains some of the elements of A but not all the elements.

2. Let A = {a, b, c, d}. Let B = {d, b, c,a}

Here B is not the proper subset of A since it contains all the elements in A. Hence it is called as the improper subset.

More information on subsets:

→ The empty set is a subset of every set.

→ Every set is a subset of itself, but it is an improper subset.

→ The number of subsets of a set is given by $2^{n}$ where n is the number of elements in the set.