Question

10. Let A = {-5, -3,-2,-1} B={-2,-1,0}, and C = {-6,-4,-2}. Find
A\(B\C) and (A\B)\C . What can we conclude about set difference operation?

Answer 1

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

SOLUTION :

GIVEN :
A = {-5,-3,-2,-1} B = {-2,-1,0} and C = {-6,-4,-2}

L.H.S :
A\(B\C)
(B\C) = {-2,-1,0} \ {-6,-4,-2}
= {-1,0}
A\(B\C) = {-5,-3,-2,-1} \ {-1,0}
A\(B\C) = {-5,-3,-2}

R.H.S :
(A\B)\C
(A\B) = {-5,-3,-2,-1} \ {-2,-1,0}
= {-5,-3}
(A\B)\C = {-5,-3} \ {-6,-4,-2}
(A\B)\C = {-5,-3}

L.H.S ≠ R.HS

A\(B\C) ≠ (A\B)\C

We conclude about set difference operation that they are not associative.


HOPE THIS WILL HELP YOU…

Answer 2

Hi ,

It is given that ,

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

B = { -2 , -1 , 0 }

C = { -6 , -4 , -2 }

A\( B\C )

= A\ ( { -2 , -1 , 0 } - { -6 , -4 , -2 } )

= { -5 , -3 , -2 , -1 } - { - 1 , 0 }

= { -5 , -3 , -2 } ---( 1 )

( A\B )\C = ( { -5 , -3 , -2 , -1 } - { -2 , -1 , 0 } ) \C

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

= { -5 , - 3 } --( 2 )

Therefore ,

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

A\( B\C ) ≠ ( A\B )\C

I hope this helps you.

: )