# SMU-bt00080 – Chapter 2

30 Questions | Total Attempts: 11

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SMU-BT00080: Algorithms hapter 2 Mathematical Functions and Notations

Related Topics
• 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