SMU-bt00080 – Chapter 2

30 Questions | Total Attempts: 11

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Mathematics Quizzes & Trivia

SMU-BT00080: Algorithms hapter 2 Mathematical Functions and Notations


Questions and Answers
  • 1. 
    If f is a function from a set A to a set B, then it can be denoted as ____________. 
    • A. 

      F: A→B

    • B. 

      F: B→A

    • C. 

      F: A←B

    • D. 

      None of the above

  • 2. 
    Let f be a function from a set A to a set B.  For x Ԑ A, f(x) is called __________ of x in B.
    • A. 

      Image

    • B. 

      Subset

    • C. 

      Domain

    • D. 

      Codomain

  • 3. 
    If f is a function from a set A to a set B, then A is called the ___________ of f .
    • A. 

      Image

    • B. 

      Subset

    • C. 

      Domain

    • D. 

      Codomain

  • 4. 
    If f is a function from a set A to a set B, then B is called the ___________ of f.
    • A. 

      Image

    • B. 

      Subset

    • C. 

      Domain

    • D. 

      Codomain

  • 5. 
    If f: xy is a function, then there may be more than one element, say x1 and x2 such that f(x1) = f(x2)
    • A. 

      True

    • B. 

      False

  • 6. 
    If f: xy is a function, then there will not be more than one element
    • A. 

      True

    • B. 

      False

  • 7. 
    By putting restriction that f(x)f(y), if x≠y on a function f: xy, we get special functions, called _____________
    • A. 

      Injective functions.

    • B. 

      Onto

    • C. 

      Subjective

  • 8. 
    A function f: AB is said to be 1 – 1 or injective function if for x, y Ԑ A, if f(x) = f(y) then ______________
    • A. 

      X = y

    • B. 

      X≠y

  • 9. 
    A function f: AB is said to be _________________ if for x, y Ԑ A, if f(x) = f(y) then x = y
    • A. 

      Injective

    • B. 

      Onto

    • C. 

      Subjective

  • 10. 
    A function f: XY is said to be _______________ if to every element of, the codomain of f, there is an element x Ԑ X such that f(x) = y.
    • A. 

      Injective

    • B. 

      1 – 1

    • C. 

      Subjective

  • 11. 
    A function f: RR is said to be _____________________ if for x, y Ԑ R and x ≤ y we have f(x) ≤ f(y).
    • A. 

      Monotonically increasing

    • B. 

      Strictly monotonically increasing

    • C. 

      Monotonically decreasing

    • D. 

      Strictly monotonically decreasing

  • 12. 
    A function f: RR is said to be ________________________ if for x, y Ԑ R and x < y we have f(x) < f(y).
    • A. 

      Monotonically increasing

    • B. 

      Strictly monotonically increasing

    • C. 

      Monotonically decreasing

    • D. 

      Strictly monotonically decreasing

  • 13. 
    A function f: RR is said to be ___________________ if for x, y Ԑ R and x ≤ y we have f(x) ≥ f(y).
    • A. 

      Monotonically increasing

    • B. 

      Strictly monotonically increasing

    • C. 

      Monotonically decreasing

    • D. 

      Strictly monotonically decreasing

  • 14. 
    A function f: RR is said to be ______________________ if for x, y Ԑ R and x < y we have f(x) > f(y).
    • A. 

      Monotonically increasing

    • B. 

      Strictly monotonically increasing

    • C. 

      Monotonically decreasing

    • D. 

      Strictly monotonically decreasing

  • 15. 
    ______________ maps each real number x to the integer, which is the greatest of all integers less than or equal to x.
    • A. 

      Floor Function

    • B. 

      Ceiling Function

    • C. 

      Exponentiation Function

    • D. 

      Polynomial Function

  • 16. 
    ______________ maps each real number x to the integer, which is the least of all integers greater than or equal to x.
    • A. 

      Floor Function

    • B. 

      Ceiling Function

    • C. 

      Exponentiation Function

    • D. 

      Polynomial Function

  • 17. 
    ______________ is a function of two variables x and n where x is any non – negative real number and n is an integer.
    • A. 

      Floor Function

    • B. 

      Ceiling Function

    • C. 

      Exponentiation Function

    • D. 

      Polynomial Function

  • 18. 
    └ –2.5┘ =
    • A. 

      2

    • B. 

      -2

    • C. 

      3

    • D. 

      -3

  • 19. 
    –2.5 =
    • A. 

      2

    • B. 

      -2

    • C. 

      3

    • D. 

      -3

  • 20. 
    Each of the floor function and ceiling function is a monotonically increasing function but not strictly monotonically increasing function.
    • A. 

      True

    • B. 

      False

  • 21. 
    Each of the floor function and ceiling function is strictly monotonically increasing function.
    • A. 

      True

    • B. 

      False

  • 22. 
    If n is a given positive integer and b is any integer, then b mod n = r where 0≤r < n and b = ______________.
    • A. 

      K * n + r

    • B. 

      N * r + k

    • C. 

      R * k + n

    • D. 

      K + n * r

  • 23. 
    B mod n = r, where r is obtained by subtracting multiplies of n so that the remainder r lies between 0 and ___________.
    • A. 

      N – 1

    • B. 

      N

    • C. 

      N + 1

    • D. 

      N*n

  • 24. 
    The concept of ______________ expectation is needed in average – case analysis of algorithms.
    • A. 

      Mathematical

    • B. 

      Analytical

    • C. 

      Algorithmic

    • D. 

      Actual

  • 25. 
    In order to understand the complexity/efficiency of an algorithm, it is very important to understand the notion of the size of ___________ of the problem under consideration and the role of size in determining complexity of the solution.
    • A. 

      An instance

    • B. 

      A process

  • 26. 
    If the size of general instance is n then time complexity of the algorithm solving the problem under consideration is some function of ____________.
    • A. 

      N

    • B. 

      N!

    • C. 

      N-1

    • D. 

      N+1

  • 27. 
    In the ______________ approach algorithm is actually executed on various instances of the problem and the size (s) and time (t) to determine the complexity.
    • A. 

      Empirical

    • B. 

      Theoretical

    • C. 

      Priori

  • 28. 
    In the ____________ approach, the complexity of the algorithm is determined mathematically.
    • A. 

      Theoretical

    • B. 

      Empirical

    • C. 

      Posterior

  • 29. 
    The notation __________ provides asymptotic upper bound for a given function.
    • A. 

      O

    • B. 

    • C. 

      θ

    • D. 

      ω

  • 30. 
    f(x) is a polynomial of degree m and g(x) is a polynomial of degree n. Then f(x) = o(g(x)) if and only if ___________.
    • A. 

      N > m

    • B. 

      N < m

    • C. 

      N = m

    • D. 

      N ≤ m