What is a subset?

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-