If all elements of set A is in set B.

So, we say

A is a subset of B

Example:

A = {
**
1, 2, 3, 4, 5
**
}

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

Since 1, 2, 3, 4, 5 is in set B as well,

So, we write

A is a subset of B.

A ⊂ B

### Let X = {1, 2, 3}, Y = {3, 4, 5}, Z = {1, 2, 3, 4, 5}

**
Is X a subset of Z?
**

-a-

Since 1, 2, 3 are in set Z

X ⊂ Z

-ea-

**
Is Y a subset of Z?
**

-a-

Since 3, 4, 5 are in set Z

Y ⊂ Z

-ea-

**
Is X a subset of Y?
**

-a-

Since 1, 2 are not in Y

∴ X is not a subset of Y

i.e. X ⊄ Y

-ea-

**
Is Y a subset of X?
**

-a-

Since 4, 5 are not in Y

∴ Y is not a subset of X

i.e. Y ⊄ X

-ea-