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  • Question
  • Write down the power set of the set {0}.


  • Options
  • A. ?
  • B. {0}
  • C. {?}
  • D. {?, {0}}

  • Correct Answer
  • {?, {0}} 

    Explanation

    Let, A = {0}. The possible subsets of this set A are ? and {0}, so the power set of the given set A is P(A) = {f, {0}}.


  • Sets and Functions problems


    Search Results


    • 1. 
      Let A = {?, {?}, 1, {1, ?}, 7}. Which of the following is false?

    • Options
    • A. ? ? A
    • B. {?} ? A
    • C. {1} ? A
    • D. {7, ?,} ? A
    • Discuss
    • 2. 
      Let A = {1, 3, 5} and B = {x: x is an odd natural number < 6}. Which of the following is false?

    • Options
    • A. A ? B
    • B. B ? A
    • C. A = B
    • D. None of these
    • Discuss
    • 3. 
      If U = {a, b, c, d, e, f}, A = {a, b, c}, find (U ? A)?.

    • Options
    • A. U
    • B. A
    • C. ?
    • D. None of these
    • Discuss
    • 4. 
      If U = {a, b, c, d, e, f}, A = {a, b, c}, B = {c, d, e, f}, C = {c, d, e}, find (A ? B) ? (A ? C).

    • Options
    • A. {c}
    • B. {a}
    • C. {b}
    • D. {d}
    • Discuss
    • 5. 
      If A and B have n elements in common, how many elements do A × B and B × A have in common?

    • Options
    • A. n
    • B. n3
    • C. n2
    • D. None of these
    • Discuss
    • 6. 
      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
    • 7. 
      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
    • 8. 
      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
    • 9. 
      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
    • 10. 
      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


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