SET THEORY PRACTICE QUESTIONS

(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

(2) Given

n(A)  =  285, n(B) = 195, n(U) = 500, n(AUB) = 410,

find n(A'UB')            Solution

(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).          Solution

(4) 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}

(ii) A  =  {a, b, c, d, e} B = {x, y, z} and C = {a, e, x}   Solution

(5) 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

(6) 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

(7) 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

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