# If A and B are subsets of the universal set U, then show that(i) A ⊂ A ∪ B(ii) A ⊂ B ⇔ A ∪ B = B(iii) (A ∩ B) ⊂ A

(i) Given: A and B are two subsets

To prove: A A B

Let x A

x A or x B

x A B

A A B

Hence Proved

(ii) Given: A and B are two sets

To prove: A B A B = B

Let x A B

x A or x B

x B { A B}

A B B…………(1)

We know,

B A B {this is always true}…………(2)

From (1) and (2):

A B = B

Now,

Let y A

y A B

y B { A B = B}

A B

So,

A B A B = B

Hence Proved

(iii) Given: A and B are two subsets

To prove: (A B) A

Let x A B

x A and x B

x A

A B A

Hence Proved

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