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  • Question
  • Which of the following sets is non-empty?


  • Options
  • A. A = set of odd natural numbers divisible by 2
  • B. B = {x : x + 5 = 0, x ? N}
  • C. C = set of even prime numbers
  • D. D = {x : 1 < x < 2, x ? N},

  • Correct Answer
  • C = set of even prime numbers 

    Explanation

    A natural number is a number that occurs commonly and obviously in nature. As such, it is a whole, non-negative number. The set of natural numbers, denoted N, can be defined in either of two ways: N = {0, 1, 2, 3, ...}
    As per given option.
    (a) As no odd natural number is divisible by 2, the set A is empty.
    (b) Since no natural number satisfies the equation x + 5 = 0,
    ? B = ?
    (c) Since 2 is an even prime number, i.e., C = {2}, C is not an empty set.
    (d) Since there is no natural number between 1 and 2, D is an empty set.


  • Sets and Functions problems


    Search Results


    • 1. 
      Which of the following sets is finite?

    • Options
    • A. I = { x : x ? Z and x2 ? 2x ? 3 = 0 }
    • B. B = The set of natural numbers which are divisible by 2
    • C. C = The set of lines passing through a point.
    • D. D = { x : x ? Z and x > - 5 }
    • Discuss
    • 2. 
      Which of the following sets is finite?

    • Options
    • A. The set of the months of a year
    • B. {1, 2, 3,?}
    • C. {1, 2, 3,? 90, 100}
    • D. The set of lines which are parallel to x-axis
    • Discuss
    • 3. 
      Which of the following sets is empty?

    • Options
    • A. A = {x: x ? n and x ? 1}
    • B. B = {x: 3x + 1 = 0, x ? N}
    • C. C = {x: x is an integer and -1 < x < 1}
    • D. D = set of months of the year beginning with F.
    • Discuss
    • 4. 
      Find the cardinal number of the following set {x: x is a natural number ? 30 and is divisible by 7 or 11}

    • Options
    • A. 4
    • B. 8
    • C. 6
    • D. 2
    • Discuss
    • 5. 
      For which of the following cases A and B are equivalent?

    • Options
    • A. A = {a, b, c,?, z}, B = {1, 2, 3,?, 24}
    • B. A = {1/3,1/2,3/5}, B = { x : x = n/n+2, n ? N}
    • C. A = {2, 4, 6}, B = {(2, 4), (4, 6), (2, 6)}
    • D. A = { x : x = ( n3 - 1 )/ ( n3 + 1) , n ? W, n ? 3} , B = { 0,7/9,13/14}
    • Discuss
    • 6. 
      Write down the power set of C = {1, {2}}.

    • Options
    • A. {?, {1}, {{2}}}
    • B. {?, {1}, {{2}}, {1, {2}}}
    • C. {{1}, {{2}}, {1, {2}}
    • D. None of these
    • Discuss
    • 7. 
      Which of the following statements is true?

    • Options
    • A. Every subset of a finite set is finite.
    • B. Every subset of an infinite set is infinite.
    • C. Every subset of an infinite set is finite.
    • D. A proper subset of a finite set is equivalent to the set itself.
    • Discuss
    • 8. 
      Let A = {x: x ? N ? x is a multiple of 2}
      B = {x: x ? N ? x is a multiple of 5}
      C = {x: x ? N ? x is a multiple of 10}
      Describe the set A ? (B ? C)

    • Options
    • A. A
    • B. B
    • C. C
    • D. None of these
    • Discuss
    • 9. 
      If U = {2, 3, 4, 5, 6, 7, 8, 9, 10, 11}, A = {3, 5, 7, 9, 11} and B = {7, 8, 9, 10, 11}, Then compute (A ? B)?.


    • Options
    • A. {2, 3, 5, 7, 9, 11, 12}
    • B. {2, 4, 6, 8, 10, 11, 12}
    • C. {2, 4, 6, 8, 9, 10, 11}
    • D. None of these
    • Discuss
    • 10. 
      If S and T are two sets such that S has 21 elements, T has 32 elements, and S ? T has 11 elements, how many elements does S ? T have?

    • Options
    • A. 52
    • B. 32
    • C. 42
    • D. None of these
    • Discuss


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