Question

Let A = ) ( (0, 1), B = (2,3,4) and c= (3,5) verity that Ax (BUC) = (AXB) U (AXC)​

Answer 1

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Answer 2

Answer:

proved , A*(B∪C) = ( A*B)∪(A*C)

Step-by-step explanation:

Given :- A = { 0,1 } , B = { 2,3,4 } , C = { 3,5 }

To find :- to verify :- A* ( B∪C) = (A*B)∪(A*C)

Solution :-

Step 1) write the sets , A = { 0,1 } , B = { 2,3,4 } , C = ( 3,5 }

Step 2)

LHS = A * ( B∪C)

1. ( B∪C) = { 2,3,4 } ∪ { 3,5}

              = { 2,3,4,5} -------( by using the union property )

2. A* ( B∪C) = { 0,1} * { 2,3,4,5}

   A * ( B ∪C) = { (0,2) ,(0,3) , ( 0,4) , (0,5) , (1,2) ,( 1,3) , ( 1,4 ) , ( 1 , 5 ) }

--------- ( by using multiplication property of sets  , multiply each element of the set with the other set )

Step 3)

RHS = (A*B) ∪ ( A*C)

1. A*B = { 0,1 } * { 2,3,4 }

         = { ( 0,2 ) , ( 0,3 ) , ( 0,4 ) , ( 1,2 ) , ( 1,3 ) , (1,4 ) } ----- (1)

2. A*C = { 0,1 } * { 3,5 }

           = { ( 0,3 ) , ( 0,5 ) , (1,3 ) , ( 1,5 ) } ------ ( 2)

3. ( A*B) ∪ ( A*C ) = { ( 0,2 ) , ( 0,3 ) , ( 0,4 ) , ( 0,5 ) , ( 1,2 ) , ( 1,3 ) , ( 1,4 ) , ( 1,5 ) }  ------ ( 3 )

Step 4)  From LHS and RHS equation ,

we conclude that LHS = RHS ,

and proved that ,

  A* ( B∪C)  =  ( A*B ) ∪  ( A*C )

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