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Sets Test - 4

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Sets Test - 4
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Weekly Quiz Competition
  • Question 1
    1 / -0

    Let A = { 1,2,3,4} , B = { 2,3,4,5,6 } , then (A∩B)is equal to :

    Solution

    Here A={1,2,3,4} and B={2,3,4,5,6}A∩B={1,2,3,4}∩{2,3,4,5,6}={2,3,4}

  • Question 2
    1 / -0

    Let A and B be two sets in the universal set . Then A - B is equal to

    Solution

    x∈A−B⇒x∈ A but x∉B⇒x∈ A but x∉(A∩B)⇒x∈A−(A∩B)⇒A−B⊆A−(A∩B)similarly  

    we can show that A−(A∩B)⊆A−B

    Hence A−B=A−(A∩B)

  • Question 3
    1 / -0
    If A and B are two finite sets such that A ∩ B is not a null set, then n (A ∪ B) is equal to
  • Question 4
    1 / -0

    Let A = { a,b,c } , B = { b,c,d } , C = { a,b,d,e } , then  A∩(B∪C) is

    Solution

    Here A={a,b,c},B={b,c,d }and C={a,b,d,e}B∪C={a,b,c,d,e}A∩(B∪C)={a,b,c}

  • Question 5
    1 / -0
    Out of 500 people in a locality, the numbers of people who buy items A, B and C are as given below: 

    Item A only - 90, item A but not B - 115, items A and C - 40, item A - 130, items B and C - 40, item C - 240, none of the three - 120.

    Find the number of people who buy A or B, but not C.
  • Question 6
    1 / -0

    Let U = { 1,2,3,4,5,6,7,8,9,10 } , A = { 1,2,5 } , B = { 6,7 }. Then A∩B′  is

    Solution

    Given U={1,2,3,4,5,6,7,8,9,10},A={1,2,5},B={6,7}B′={1,2,3,4,5,8,9,10}A∩B′={1,2,5}=A

  • Question 7
    1 / -0
    The set (A U B U C) ∩ (A ∩ Bc ∩ Cc)c ∩ Cc is equal to
  • Question 8
    1 / -0
    Let A be the set of all determinants of order 3 with entries 0 or 1 only, B the subset of A consisting of all determinants with value 1 and C the subset consisting of all determinants with value - 1. Which of the following options is correct?
  • Question 9
    1 / -0

    Let A and B be two sets such that n(A)=35,n(B)=42 and n(A∩B)=17, find n(A−B)

    Solution

    ​​​​Given that n(A∩B)=17 We have A−B=A−(A∩B) Therefore n(A−B)=n(A)−n(A∩B)=35−17=18

  • Question 10
    1 / -0
    In a party, 40 people drank tea, 30 people drank coffee, 25 people drank juice, 15 people drank tea and coffee, 12 people drank juice and tea, 8 people drank coffee and juice and 5 people drank all the three. How many people drank only coffee?
  • Question 11
    1 / -0

    If A and B are two sets, then A∩(A∪B)′ is equal to

    Solution

    A∩(A∪B)′=ϕ

    since (A∪B)′ Set represent the element which are not belongs to it,so there is no common element with the set A.So the answer is null set

  • Question 12
    1 / -0
    In a town with a population of 5000, the number of people who are egg-eaters is 3200. If 2500 are meat-eaters and 1500 eat both egg and meat, then how many of them eat neither meat nor egg?
  • Question 13
    1 / -0
    Two finite sets have m and n elements. The total number of subsets of the first set is 56 more than the that of subsets of the second set. The values of m and n respectively are
  • Question 14
    1 / -0
    In a zoo, there are 42 animals in the first sector, 34 in the second sector and 20 in the third sector. Out of these, 24 graze in sector one and sector two, 10 graze in sector two and sector three and 12 graze in sector one and sector three. These figures also include four animals grazing in all the three sectors. Find the total number of animals.
  • Question 15
    1 / -0
    In a survey conducted among 60 managers, it was found that 25 read Business India, 30 read Business World, 24 read Business Today, 10 read Business India and Business World, 9 read Business India and Business Today, and 12 read Business World and Business Today. If 5 read all the three, how many of them read only one publication? (Assume that each of them reads one of the given publications.)
  • Question 16
    1 / -0
    Out of 500 people in a locality, the number of people who buy items A, B and C is given below.

    Item A only - 90, item A but not B - 115, items A and C - 40, item A -130, items B and C - 40, item C - 240, none of the three - 120. How many people buy only item B?
  • Question 17
    1 / -0
    Directions: Out of 500 people in a locality, number of people who buy items A, B and C is as given below:

    Item A only - 90, item A but not B - 115, items A and C - 40, item A - 130, items B and C - 40, item C - 240, none of the three - 120. The frequencies of which of the following are equal?
  • Question 18
    1 / -0

    If A and B be any two sets , then (A∪B)′  is equal to

    Solution

    x∈(A∪B)′⇒x∉(A∪B)⇒x∉A or x∉B⇒x∈A′ and x ∈B′⇒x∈A′∩B′⇒(A∪B)′⊆A′∩B′

    Similarly we can show (A′∩B′)⊆(A∪B)′

    so (A∪B)′=(A′∩B′)

  • Question 19
    1 / -0

    If A and B be any two sets , then (A∩B) ‘ is equal to

    Solution

    x∈A′∪B′⇒x∈A′or x∈B′⇒x∉A or x∉B⇒x∉A∩B⇒x∉(A∩B)A′∪B′⊆(A∩B)′Hence(A∩B)′=A′∪B′


    alternatively by De morgans Law (A′∪B′)=(A∩B)′

  • Question 20
    1 / -0

    If A and B are two sets , then A∪B=A∩B if

    Solution

    Let A=B,Then,A∪B=A and A∩B=A⇒A∪B=A∩B
    Thus ,A=B⇒A∪B=A∩B....(2)
    Conversely,let A∪B=A∩B,now we have to prove that A=B.
    Let x∈A⇒x∈A∪B⇒x∈A∩B⇒x∈A and x∈B⇒x∈B so, A⊂B.....(2)
    Let y∈B⇒y∈A∪B⇒y∈A∩B⇒y∈A and y∈B⇒y∈A So,B⊂A.....(3)Thus,A∪B=A∩B⇒A=B.....(4)From(1)and(4),we get A∪B=A∩B⇔A=B

  • Question 21
    1 / -0
    Let R be set of points inside a rectangle of sides a and b (a, b > 1) with two sides along the positive direction of x-axis and C be the set of points inside a unit circle, then which of the following statements is true?
  • Question 22
    1 / -0
    The shaded area in this diagram represents 

  • Question 23
    1 / -0
    In a college, 40% of the students play basketball, 34% play tennis and 234 play both the sports. The number of students who play neither basketball nor tennis is 52% of the total students. What is the total number of students in the college?
  • Question 24
    1 / -0
    In a survey of political preference, people were asked to give their preference on three government proposals I, II and III. 78% were in favour of atleast one of the proposals, 50% favoured proposal I, 30% favoured proposal II and 20% favoured proposal III. If 5% favoured all the three proposals, what percent of people favoured more than one of the three proposals?
  • Question 25
    1 / -0

    If A is any set , then

    Solution

    A∪A′={x∈U:x∈A}∪{x∈U:x∉A}=U

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