Q. 64.2( 12 Votes )

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

Answer :

(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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