SET THEORY PRACTICE QUESTIONS

Question 1 :

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 (AUBUC).

Solution

Question 2 :

verify

n(AUBUC)

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

(i) A  =  {4, 5, 6}, B  =  {5, 6, 7, 8} and C  =  {6, 7, 8, 9}

Solution

Question 3 :

If the sets A and B are given by

A = {1, 2, 3, 4}

B = {2, 4, 6, 8, 10}

and the universal set

U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}

then :

(a) (A 𝖴 B)' = {5, 7, 9}      (b) (A ∩ B)'= {1, 3, 5, 6, 7}

(c) (A ∩ B)' = {1, 3, 5, 6, 7, 8}     (d) None of these

Solution

Question 4 :

If A = {1, 2, 3, 4}, B = {2, 3, 5, 6} and C = {3, 4, 6, 7}, then

(a) A – (B ∩ C) = {1, 3, 4}        (b) A – (B ∩ C) = {1, 2, 4}

(c) A – (B 𝖴 C) = {2, 3}       (d) A – (B 𝖴 C) = {Ø}

Solution

Question 5 :

Given the sets A = {1, 3, 5}, B = {2, 4, 6} and C = {0, 2, 4, 6, 8}. Which of the following may be considered as universal set for all the three sets A, B and C:

(a) {0, 1, 2, 3, 4, 5, 6}           (b) Ø

(c) {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10}

(d) {1, 2, 3, 4, 5, 6, 7, 8}

Solution

Question 6 :

From 50 students taking examination in Mathematics, Physics and Chemistry, each of the students has passed in at least one of the subject, 37 passed Mathematics, 24 Physics and 43 Chemistry. Atmost 19 passed Mathematics and Physics, atmost 29 Mathematics and Chemistry and atmost 20 Physics and Chemistry. Then, the largest numbers that could have passed all three examinations, are:

(a) 12      (b) 14     (c) 15      (d) 16

Solution

Question 1 :

In a college, 60 students enrolled in chemistry,40 in physics, 30 in biology, 15 in chemistry and physics,10 in physics and biology, 5 in biology and chemistry. No one enrolled in all the three. Find how many are enrolled in at least one of the subjects.

Solution

Question 2 :

In a town 85% of the people speak Tamil, 40% speak English and 20% speak Hindi. Also 32% speak English and Tamil, 13% speak Tamil and Hindi and 10% speak English and Hindi, find the percentage of people who can speak all the three languages.

Solution

Question 3 :

An advertising agency finds that, of its 170 clients, 115 use Television, 110 use Radio and 130 use Magazines. Also 85 use Television and Magazines, 75 use Television and Radio, 95 use Radio and Magazines, 70 use all the three. Draw Venn diagram to represent these data. Find 

(i) how many use only Radio ?

(ii) how many use only Television ?

(iii) how many use Television and Magazine but not radio?

Solution

Question 4 :

In a group of students, 65 play foot ball, 45 play hockey, 42 play cricket, 20 play foot ball and hockey, 25 play foot ball and cricket, 15 play hockey and cricket and 8 play all the three games. Find the total number of students in the group (Assume that each student in the group plays at least one game).

Solution

Question 5 :

A survey of faculty and graduate students at the University of Florida's film school revealed the following information: 51 admire Moe 49 admire Larry 60 admire Curly 34 admire Moe and Larry 32 admire Larry and Curly 36 admire Moe and Curly 24 admire all three of the Stooges 1 admires none of the Three Stooges

a) How many people were surveyed? 

b) How many admire Curly, but not Larry nor Moe?

c) How many admire Larry or Curly?

d) How many admire exactly one of the Stooges?

e) How many admire exactly two of the Stooges?

Solution

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