operations on sets

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operation of sets as in mathematics is shown

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OPERATIONS ON SETS

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There are some operations which when performed on two sets give rise to another set. We will now define certain operations on sets and examine their properties. Henceforth, we will refer all our sets as subsets of some universal set.

UNION OF SETS:

UNION OF SETS Let A and B two sets. The union of A and B is the set of all those elements which belong either to A or to B or to both A and B. The symbol ‘ ’ is used to denote the union. Symbolically, we write A  B and usually read as ‘A union B’. Thus, A  B = { x : x  A or x  B}. Clearly, x  A  B  x  A or x  B. And, x  A  B  x  A and x  B.

PROPERTIES OF THE OPERATION OF UNION:

PROPERTIES OF THE OPERATION OF UNION A  B = B  A (Commutative law) (A  B)  C = A  (B  C) (Associative law) A   = A (Law of identity element,  is the identity of  ) A  A = A (Idempotent law) U  A = U (Law of U)

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Let A and B be two sets. The intersection of A and B is the set of all those elements that belong to both A and B. The symbol ‘  ’ is used to denote the intersection. Symbolically, we write A B = { x : x A and x B}. Clearly , x A B  x  A B. INTERSECTION OF SETS

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PROPERTIES OF THE OPERATION OF INTERSECTION A  B = B  A (Commutative law) (A  B)  C = A  (B  C) (Associative law) A   =  , U  A=A (Law of  and U ) A  A = A (Idempotent law) A (B C) = (A B) (A C) (Distributive Law )

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Let A and B be two sets. The difference of A and B is the set of all those elements of A which do not belong to B. Symbolically, we write A  B and read as “A minus B”. Thus, A  B = { x : x A and x B} Or, A  B = {x A : x B} Clearly, x  A  B  x  A and x  B. DIFFERENCE OF SETS

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FOR WATCHING THE PRESENTATION

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MADE BY- SUBHANKAR BRAHMA XI-C KENDRIYA VIDYALAYA NO.2, DELHI CANTT.- 10 (II shift)

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