Q. 11 B5.0( 2 Votes )

For A = {- 3,- 1,

Answer :

(ii) A (B C) = (A B) (A C)


L.H.S.


The statement A (B C) can be split into two parts for ease of solving. So using the given data first we will find the intersection of B and C then again we have to find the intersection between A and the results obtained from the intersection of B and C


Data given


A = {-3,-1, 0, 4, 6, 8, 10}


B = {-1,-2, 3 , 4, 5, 6}


C = {-1, 2, 3, 4, 5, 7}


So (B C) = {- 1, - 2, 3, 4, 5, 6} {- 1, 2, 3, 4, 5, 7}


= {-1,-2, 3, 4, 5}


Now A (B C) = {- 3, - 1, 0, 4, 6, 8, 10} {-1,-2, 3, 4, 5}


= {-1, 4}……………………. (i)


R.H.S


The statement (A B) (A C) can be split into three parts for ease of solving. First we will find the intersection between A, B and A, C then again we will do intersection operation between the results obtained from the intersection of A, B and A, C.


(A B) = {- 3, - 1, 0, 4, 6, 8, 10} {- 1, - 2, 3, 4, 5, 6}


= {-1, 4, 6}


(A C) = {- 3, - 1, 0, 4, 6, 8, 10} {- 1, 2, 3, 4, 5, 7}


= {-1, 4}


(A B) (A C) = {-1, 4, 6} {-1, 4}


= {-1, 4}…………………….. (ii)


From statement (i) and (ii) its verified that L.H.S equals to R.H.S


I.e. A (B C) = (A B) (A C)


Venn diagram for A (B C) = (A B) (A C)






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