Question

4. If A = {4,6,7,8,9}, { B = 2,4,6} and C = {1,2,3,4,5,6}, then find
(i) A+(B+C) (ii) A+(B + C) (iii) A\(C\B)

Answer 1

Question:
If A = {4,6,7,8,9} , B = {2,4,6} and C = {1,2,3,4,5,6},then find
(i) A U (B ∩ C) (ii) A ∩ (B U C) (iii) A \ (C \ B)


Union of two sets :
The union of the sets A and B is the set of all the element that belongs to either A or B or both. It is denoted by A U B(“A union B”).

Intersection of two sets :
The intersection of the sets a and b is the set of all the elements which belong to both A and B. It is denoted by A ∩ B (“ A intersection B”).
•if a and b do not have any element in common then A ∩ B= a null set = Ø

SOLUTION:
(i) A U (B ∩ C)
(B ∩ C) = {2,4,6} ∩ {1,2,3,4,5,6}
= {2,4,6}
A U (B ∩ C) = {4,6,7,8,9} U {2,4,6}
A U (B ∩ C) = {2,4,6,7,8,9}

(ii) A ∩ (B U C)
(B U C) = {2,4,6} U {1,2,3,4,5,6}
= {1,2,3,4,5,6}
A ∩ (B U C) = {4,6,7,8,9} ∩ {1,2,3,4,5,6}
A ∩ (B U C) = {4,6}

(iii) A \ (C \ B)
C \ B = {1,2,3,4,5,6} \ {2,4,6}
= {1,3,5}
A \ (C \ B) = {4,6,7,8,9} \ {1,3,,5}
A \ (C \ B) = {4,6,7,8,9}

HOPE THIS WILL HELP YOU….

Answer 2

Hi,

It is given that,

A = { 4, 6, 7, 8 , 9 }

B = { 2 , 4 , 6 }

C = { 1, 2 , 3 , 4, 5 , 6 }

****************************************

we know that ,

A U B = { x / x € A or x € B }

A and B = { x / x € A and x € B }

A/B = { x /x € A and x doesn't belongs to B }

*****************************************

i ) A U ( B U C )

= A U ( { 2, 4 , 6 } U { 1, 2 , 3 , 4 , 5 , 6 } )

= A U { 1 , 2 , 3 , 4 , 5 , 6 }

= { 4, 6, 7 , 8 , 9 } U { 1,2,3,4,5,6 }

= { 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 } ---( 1 )

ii ) ( A U B ) U C

= ( { 4,6,7,8,9 } U { 2,4,6 } ) U C

= { 2,4,6,7,8,9 } U C

= { 2,4,6,7,8,9 } U { 1,2,3,4,5,6}

= { 1,2,3,4,5,6,7,8,9 } ---( 2 )

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

A U( B UC ) = ( A U B ) U C

[ associative proporty ]

iii )

A\( C\B )

= A \ ( { 1,2,3,4,5,6 } \{ 2, 4 ,6 })

= A \ { 1 , 3 , 5 }

= { 4, 6 , 7 , 8 , 9 } \ { 1 , 3 , 5 }

= { 4 , 6, 7 , 8 , 9 }

I hope this helps you.

: )