Question

9. 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 1

•A\B means removing all elements of  B from A.

SOLUTION :
GIVEN :
A = {5,10,15,20}

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

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

L.H.S :
A\(B\C)

(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}

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

R.H.S :
(A\B) = {5,10,15,20}\{6,10,12,18,24}
= {5,15,20}

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

(A\B)\C = {5,15,20}

A\ (B\C) ≠ (A\B)\C

L.H.S ≠ R.H.S

HOPE THIS WILL HELP YOU...

Answer 2

Hi ,

It's given that

A = { 5 , 10 , 15 }

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

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

LHS = A\( B\C )

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

= A\{ 6 , 18 , 24 }

= { 5, 10 , 15 , 20 } \ { 6 , 18 , 24 }

= { 5 , 10 , 15 , 20 } -------( 1 )

RHS = ( A\B ) \C

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

= { 5, 15, 20 } \{ 7, 10, 12, 14, 21, 28 }

= { 5, 15, 20 } ---( 2 )

Therefore ,

from ( 1 ) and ( 2 ) , we conclude that

LHS ≠ RHS

I hope this helps you.

: )