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Sets Test - 5

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Sets Test - 5
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Weekly Quiz Competition
  • Question 1
    1 / -0

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

    Solution

    HereA={a,b,c},B={b,c,d}andC

    ={a,b,d,e}

    B∪C={a,b,c,d,e}

    A∩(B∪C)={a,b,c}

  • Question 2
    1 / -0

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

    Solution

    Let \(x \in A\)

    \( \Rightarrow x \in A \cup B\), [\(\because\) \(A \subseteq A \cup B]\)

    \(x \in A \cap B\),  [As \(A \cup B=A \cap B]\)

    \(x \in A\) and \(x \in B \)

    \(\Rightarrow x \in A\)

    \(B \subseteq A\)

    Now, \(A \subseteq B\) and \( B \subseteq A \)

    \(\Rightarrow A=B\)

    Hence, the correct option is (A).

  • Question 3
    1 / -0
    The power set of {2, 5} is
  • Question 4
    1 / -0

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

    Solution

    x∈(A∪B)′

    ⇒x∉(A∪B)

    ⇒x∉Aorx∉B

    ⇒x∈A′andx∈B′

    ⇒x∈A′∩B′

    ⇒(A∪B)′⊆A′∩B′ 


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


    so (A∪B)′=(A′∩B′)

  • Question 5
    1 / -0
    In a town, 48% people are educated, 51% people are young, 60% are servicemen, 24% are educated and young. There are 25% are young and servicemen, 27% are educated and servicemen and 5% fit in all the three categories. What is the ratio of educated or young, but not servicemen to young or servicemen but not educated?
  • Question 6
    1 / -0

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


    Solution

    HereA={1,2,3,4}andB={2,3,4,5,6}

    A∩B={1,2,3,4}∩{2,3,4,5,6}

    ={2,3,4}

  • Question 7
    1 / -0
    If A  B then for a non-empty set C,
  • Question 8
    1 / -0
    Which of the following is an empty set?
  • Question 9
    1 / -0

    Which of the following is a null set ?


    Solution

    x2+1=0

    ⇒x2=−1

    ⇒x2=√−1

    ⇒x=i∈C 

    [i=imaginory root of unity which is a complex no.]

    since the solution of x doesnot belongs to real no hence the set is null set


     
  • Question 10
    1 / -0
    If Na = {an : n  N}, find the value of N6  N8.
  • Question 11
    1 / -0

    Two sets A and B are said to be disjoint iff

    Solution

    Two sets are called disjoint if and only if these two set have no common element i.e A∩B=∅

  • Question 12
    1 / -0
    The set (A ∩ Bc)c ∪ (B ∩ C) is equal to
  • Question 13
    1 / -0
    If A  B, B  A then
  • Question 14
    1 / -0
    Given that aN = {ax : x  N} and bN  cN = dN, where b, c  N and b, c are co-prime to each other.
    Which of the following conditions is true according to the statement given above?
  • Question 15
    1 / -0
    If A = {letters of the word xerox} and B = {x, y, z, w}, then find A  B.
  • Question 16
    1 / -0
    In a meeting of 100 people, there were 23 Indian men and 29 Indian women. Of these Indian people, 4 were dentists and 24 were either men or dentists. Assuming that there were no foreign dentists, find the number of female dentists who attended the meeting.
  • Question 17
    1 / -0
    In a group of 50 persons, everyone takes either tea or coffee. If 35 persons take tea and 25 persons take coffee, then the number of persons who take tea only (and not coffee) is
  • Question 18
    1 / -0

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

    Solution

    LetA={1,2,3,4}andB={1,2,3,4,5,6}

    HereA∩B={1,2,3,4}

    NowA∪(A∩B)={1,2,3,4,}=A

  • Question 19
    1 / -0

    If A is any set , then


    Solution

    A∪A′={x∈U:x∈A}∪{x∈U:x∉A}

    =U

  • Question 20
    1 / -0
    For any two sets A and B, A = B is equivalent to
  • Question 21
    1 / -0
    If A = {x: – 2  x  2, x  integers} and B = {x: – 3  x  3, x  integers}, then find A  B.
  • Question 22
    1 / -0
    If X = {4n – 3n – 1 : n  N} and Y = {9 (n – 1) : n  N}, then which of the following is equal to X U Y?
  • Question 23
    1 / -0
    If A = {1, 2, 3}, B = {3, 4} and C = {4, 5, 6}, find A  (B ∩ C).
  • Question 24
    1 / -0

    If A ⊆B , then A∩B is equal to

    Solution

    A ⊆B means Set A is contained in the set B.So common region is The Set A

  • Question 25
    1 / -0

    If A ⊆B , then A∪B is equal to

    Solution

    A ⊆B refers to A set is contained in the Set B.So Set B is bigger.So union the sets will be B

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