Set Theory Practice Solution4





In this page set theory practice solution4 we are going to see solution of practice questions from the worksheet set theory practice questions2.

Question 1:

If A and B are two sets and U is the universal set such that n (U) = 700, n (A) = 200, n(B) = 300 and n (A ∩ B) = 100,find n (A' ∩ B').

Solution:

n (U) = 700

n (A) = 200

n(B) = 300

n (A ∩ B) = 100

n (A' ∩ B') = n (A U B)'

To find n (A U B)' we have to use the formula for n (A U B)

n (A U B) = n (A) + n (B ) - n (A ∩ B)

              = 200 + 300 - 100

              = 500 - 100

              = 400

n (A U B)' = n (U) - n (A U B)

              = 700 - 400

              = 300

n (A' ∩ B') = n (A U B)'

n (A' ∩ B') = 300


Question 2:

Given n (A) = 285,n (B) = 195,n (U) = 500,n (A U B) = 410,find n (A' U B')

Solution:

n (A) = 285

n (B) = 195

n (U) = 500

n (A U B) = 410

n (A' U B') = n (A ∩ B)'

To find n (A ∩ B)' first we have to find n (A ∩ B)

n (A ∩ B) = n (A) + n (B) - n (A U B)

             = 285 + 195 - 410

             = 480 - 410

             = 70

n (A ∩ B)' = n (U) - n (A ∩ B)

              = 500 - 70

n (A ∩ B)' = 430      


Question 3:

For any three sets A,B and C if n (A) = 17, n (B) = 17, n(C)=17,n(A∩B) = 7,n (B∩C) = 6 , (A ∩C)= 5 and n (A ∩ B ∩ C) = 2,find n (A U B U C).

Solution:

n (A) = 17

n (B) = 17

n (C)=17

n (A ∩ B) = 7

n (B ∩ C) = 6

(A ∩ C)= 5 

n (A U B U C) = n (A)+n (B)+n (C)-n (A∩B)-n (B∩C)-n (A∩C)+n (A ∩ B ∩C)

                   = 17 + 17 + 17 - 7 - 6 - 5 + 2

                   = 53 - 18 + 2

                   = 55 - 20

n (A U B U C) = 35

set theory practice solution4 set theory practice solution4