Q. 95.0( 1 Vote )

For A = {5,10,15, 20}; B = {6,10,12,18,24} and C = {7,10,12,14,21,28},| verify whether A \ (B \ C) = (A \ B) \ C. Justify your answer.

Answer :

The given statement A \ (B \ C) = (A \ B) \ C can be rewritten as


A \ (B\C) = (A \ B) \ C.


Here we have to compare the elements obtained from the difference or compliment of two sets and check whether they are associative in nature or not.


Given data


A = {5, 10, 15, 20};


B = {6, 10, 12, 18, 24}


C = {7, 10, 12, 14, 21, 28}


L.H.S


For easy solving we can spit the statement A \ (B\C) into two halves where first we will find the difference between B and C after we will find difference between set A and the result obtained from the difference of B and C


So (B\C) = {6, 10, 12, 18, 24} \ {7, 10, 12, 14, 21, 28}


= {6, 18, 24}


A \ (B\C) = {5, 10, 15, 20} \ {6, 18, 24}


= {5, 10, 15, 20}…………. (i)


R.H.S


(A \ B) \ C again we will split this statement in two to find the difference result. First of all we will find the difference between A and B and after that another difference operation will be done between the results obtained from (A \ B) and C


Using the data given


(A \ B) = {5, 10, 15, 20} \ {6, 10, 12, 18, 24}


= {5, 10, 15, 20}


(A \ B) \ C = {5, 10, 15, 20} \ {7, 10, 12, 14, 21, 28}


= {5, 15, 20}…………. (ii)


From (i) and (ii) it’s clear that L.H.S. and R.H.S aren’t same so


A \ (B\C) = (A \ B) \ C is a false statement.


i.e A \ (B\C) ≠ (A \ B) \ C


Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.