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)
Rate this question :


For A = {- 3,- 1,
Tamil Nadu Board - MathLet A = {- 5, - 3
Tamil Nadu Board - MathGiven P = {a, b,
Tamil Nadu Board - MathFor A = {5,10,15,
Tamil Nadu Board - MathFor A = {x | x is
Tamil Nadu Board - MathFor A = {- 3,- 1,
Tamil Nadu Board - MathVerify the commut
Tamil Nadu Board - MathGiven A = {a,x,y,
Tamil Nadu Board - Math