Question

If U = {x I x ∈ N, x < 10}, A = {2x I x ∈ N, x < 5} and B = {1, 3, 4, 5}, then find (A ∪ B)' and (A ∩ B)'.

Answer 1

Hi ,

i ) U = { x/x€N, x < 10 }

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

ii ) A = { 2x/x€N , x<5 }

A = { 2,4,6,8 }

iii ) B = { 1, 3 , 4 , 5 }

iv ) AUB = { 2,4,6,8 } U { 1,3,4,5 }

= { 1,2,3,4,5,6,8 }

v ) ( A U B )'

= U - ( A U B )

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

= { 7 , 9 } ------( 1 )

vi ) A intersection B

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

= { 1 , 3 , 4 , 5 }

vii ) ( A intersection B )'

= U - ( A intersection B )

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

= { 2, 6 , 7,8,9 }

I hope this helps you.

: )