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CuriousTab

CuriousTab

Sets and Functions problems


  • 1. 
    If P = { 1, 2, 3 } and Q = { 4 , 5 } then what is the value of P × Q?

  • Options
  • A. { (4 , 5) , (1 , 5) , (2 , 4) , (2 , 5) , (3 , 4) , (3 , 5) }
  • B. { (1 , 4) , (4 , 5) , (2 , 4) , (2 , 5) , (3 , 4) , (3 , 5) }
  • C. { (1 , 4) , (1 , 5) , (2 , 4) , (3 , 5) , (3 , 4) , (3 , 5) }
  • D. { (1 , 4) , (1 , 5) , (2 , 4) , (2 , 5) , (2 , 4) , (3 , 5) }
  • Discuss
  • 2. 
    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
  • 3. 
    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
  • 4. 
    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
  • 5. 
    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
  • 6. 
    Let A = {?, {?}, 1, {1, ?}, 7}. Which of the following is false?

  • Options
  • A. ? ? A
  • B. {?} ? A
  • C. {1} ? A
  • D. {7, ?,} ? A
  • Discuss
  • 7. 
    Write down the power set of the set {0}.

  • Options
  • A. ?
  • B. {0}
  • C. {?}
  • D. {?, {0}}
  • Discuss
  • 8. 
    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
  • 9. 
    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
  • 10. 
    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

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