What is Subset? Chapter 1

**What is a Subset?** If A & B are two sets, A is called a subset of B, written A ⊆ B, if, and only if, any

element of A is also an element of B.

Symbolically:

A ⊆ B

EXAMPLES:

Let

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

C = {1, 2, 3, 4} D = {3, 1, 5}

Then

A ⊆ B ( Because every element of A is in B )

C ⊆ B ( Because every element of C is also an element of B )

A ⊆ D ( Because every element of A is also an element of D and also note

that every element of D is in A so D ⊆ A )

and A is not subset of C .

( Because there is an element 5 of A which is not in C )

If A & B are two sets, A is called a subset of B, written A ⊆ B, if, and only if, any

element of A is also an element of B.

Symbolically:

A ⊆ B

EXAMPLES:

Let

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

C = {1, 2, 3, 4} D = {3, 1, 5}

Then

A ⊆ B ( Because every element of A is in B )

C ⊆ B ( Because every element of C is also an element of B )

A ⊆ D ( Because every element of A is also an element of D and also note

that every element of D is in A so D ⊆ A )

and A is not subset of C .

( Because there is an element 5 of A which is not in C )

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