Question

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Answer 1

$\bf\huge\underline{\underline{ Given :- }}$

• U = {x:x = 2n , n $\in$ W , n<9 }

• A = { y :y = 4n , n $\in$ N , n < 2 }

• B = { z : z = 8n , n $\in$ W , n ≤ 2 }

$\bf\huge\underline{\underline{ To \: Find:- }}$

• A'

• B '

• ( A U B ) '

• ( A $\cap$ B ) '

$\bf\huge\underline{\underline{ Answer :- }}$

• U = { 0 , 2 , 4 , 6 , 8, 10, 12 ,14 ,16 }

• A = { 4 }

• B = { 8, 16 }

A' $\red{\implies}$ U - A

• $\red{\implies}$ { 0 , 2 , 4 , 6 , 8, 10, 12 ,14 ,16 } - { 4 }

• $\red{\implies}$ { 0 , 2 , 6 , 8, 10, 12 ,14 ,16 }

B' $\red{\implies}$U - B

• $\red{\implies}${ 0 , 2 , 4 , 6 , 8, 10, 12 ,14 ,16 } - { 8 , 16 }

• $\red{\implies}$ { 0 , 2 , 4 , 6 , 10, 12 ,14 }

( A U B ) ' $\red{\implies}$ U - A U B

• $\red{\implies}$ { 0 , 2 , 4 , 6 , 8, 10, 12 ,14 ,16 } - { 4 , 8 , 16}

• $\red{\implies}$ { 0 , 2 , 6 , 10, 12 ,14 }

(A $\cap$ B) ' $\red{\implies}$ U - (A $\cap$ B)

• $\red{\implies}$ { 0 , 2 , 4 , 6 , 8, 10, 12 ,14 ,16 } - { $\emptyset$ }

• $\red{\implies}$ { 0 , 2 , 4 , 6 , 8, 10, 12 ,14 ,16 }