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.
Related Videos
Heights and Distances-IHeights and Distances-IHeights and Distances-I45 mins
Resources and Development RevisionResources and Development RevisionResources and Development Revision28 mins
Cube and CuboidCube and CuboidCube and Cuboid41 mins
History - Concept and QuestionsHistory - Concept and QuestionsHistory - Concept and Questions57 mins
Sphere and HemisphereSphere and HemisphereSphere and Hemisphere16 mins
Right Circular Cone And FrustumRight Circular Cone And FrustumRight Circular Cone And Frustum43 mins
Corrosion: Types, Pros and ConsCorrosion: Types, Pros and ConsCorrosion: Types, Pros and Cons41 mins
Right Circular CylinderRight Circular CylinderRight Circular Cylinder45 mins
Revision on Substitution and  Elimination MethodRevision on Substitution and  Elimination MethodRevision on Substitution and Elimination Method44 mins
Area Related to Circles- Important Formula and ConceptsArea Related to Circles- Important Formula and ConceptsArea Related to Circles- Important Formula and Concepts59 mins
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
caricature
view all courses
RELATED QUESTIONS :

For A = {- 3,- 1,Tamil Nadu Board - Math

Let A = {- 5, - 3Tamil Nadu Board - Math

Given P = {a, b, Tamil Nadu Board - Math

For A = {5,10,15,Tamil Nadu Board - Math

For A = {x | x isTamil Nadu Board - Math

For A = {- 3,- 1,Tamil Nadu Board - Math

Verify the commutTamil Nadu Board - Math

Given A = {a,x,y,Tamil Nadu Board - Math