WASEIAN: Discrete Structures for Computer Science

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Question 1:

Let R be relation defined as R ={ <x,y>/ x - y is divisible by m,a positive integer}

Which of the following is true?

Select one:

a. R is only reflexive

b. R is neither reflexive nor symmetric

c. R is reflexive and symmetric

d. R is R is reflexive, symmetric and transitive

Correct Answer: D

Question 2:

Consider the recurrence relation : a(n) =2 a(n-1) + a(n- 3)

Then the order of the characteristic polynomial of this recurrence relation is

Select one:

a. We can not determine

b. 2

c. 1

d. 3

Correct Answer: D

Question 3:

A relation R: S to S is called a partial order relation if it is

Select one:

a. Reflexive, Antisymmetric, Transitive

b. Irreflexive,Transitive, Antisymmetric

c. Reflexive,Transitive,Symmetric

d. only Reflexive, Transitive

Correct Answer: A

Question 4:

Consider the following diagram. And choose the correct option from the given

Select one:

a. This is not a lattice

b. represents a improper lattice

c. Represent a proper lattice

d. Does not represent a poset

Correct Answer: C

Question 5:

How many ways are there to distribute six indistinguishable balls into nine distinguishable bins?

Select one:

a. 3003

b. 3000

c. 3030

d. 3300

Correct Answer: A

Question 6:

Let F be the function such that F(n) is the sum of the first n positive integers. Give a recursive definition of F(n).

Select one:

a. f(0) = 1, f(n) = f(n − 1) - n for n ≥ 1

b. f(0) = 0, f(n) = f(n − 1) + n for n ≥ 1

c. f(0) = 0, f(n) = f(n + 1) + n for n ≥ 1

d. f(0) = 1, f(n) = f(n + 1) - n for n ≥ 1

Correct Answer: B

Question 7:

Which of the following represents the Hasse diagram of the the relation ({1,2,3},less than or equal to )

Select one:

Correct Answer: C

Question 8:

What is the generating function for the finite sequence 2, 2, 2, 2, 2, 2

Select one:

a. f (x) = 2(x2−1)/(x6−1)

b. f (x) = 2(x2−1)/(x−1)

c. f (x) = 2(x2−1)/(x2−1)

d. f (x) = 2(x6−1)/(x−1)

Correct Answer: D

Question 9:

Which of the following is true?

Select one:

a. Composition of functions is NOT associative

b. Composition of functions is NOT commutative

c. Composition of functions is Associative

d. Composition of functions is commutative

Correct Answer: D

Question 10:

Which of the following is True?

Select one:

a. Then recurrence relation a(n) = a(n-1) + a(n-2) is neither linear nor homogeneous

b. Then recurrence relation a(n) = a(n-1) + a(n-2) is always linear and non homogeneous

c. Then recurrence relation a(n) = a(n-1) + a(n-2) is always non linear and homogeneous

d. Then recurrence relation a(n) = a(n-1) + a(n-2) is always linear and homogeneous

Correct Answer: D

Question:

Let m be an integer with m > 1. R on the set of integers is an equivalence relation if

Select one:

a. {(a, b) | a ≡ b (mod m)}

b. {(a, b) | a ≡ a (mod b)}

c. {(a, b) | b ≡ b (mod a)}

d. {(a, b) | b ≡ a (mod m)}

The Correct answer is: {(a, b) | a ≡ b (mod m)}

Question:

Consider the statement: ∀ x, y E Z if both xy and x + y are even, then

Select one:

a. both x and y are odd

b. both x and y are even

c. x is even and y is odd

d. x is odd and y is even

The Correct answer is:both x and y are even

Question:

If A = {0, 1}, B = {1, 2}, and C = {0, 1, 2} then what of the following isn’t in A × B × C ?

Select one:

a. (1, 1, 0)

b. (2, 2, 0)

c. (1, 1, 1)

d. (1, 2, 2)

The Correct answer is: (2, 2, 0)

Question:

Let A, B, and C be sets. Identify the the correct one among the following

Select one:

a. None of these

b. A ∩ (B ∩ C) = (C ∪ B) ∪ A

c. A ∪ (B ∩ C) = (C ∪ B) ∩ B

d. A ∩ (B ∪ C) = (C ∩ B) ∩ A

The Correct answer is: None of these

Question:

Let f1 and f2 be functions from R to R such that f1(x) = x2 and f2(x) = x − x2. What are

the functions f1 + f2 and f1 f2?

Select one:

a. x2 and x4 – x3

b. x and x3 – x2

c. x3 and x2 – x3

d. x and x3 − x4

The Correct answer is: x and x3 − x4

Question:

Determine for what of the following for “f” is not a one-to-one function:

Select one:

a. f for f (x) = x + 1 from the set of real numbers to itself

b. f from {a, b, c, d} to {1, 2, 3, 4, 5} with f (a) = 4, f (b) = 5, f (c) = 1, and f (d) = 3

c. f for f (x) = x2 from Z to the set of integers

d. f for f (x) = x2 from Z+ to the set of integers

The Correct answer is: f for f (x) = x2 from Z to the set of integers

Question:

Which of the following is not a logical equivalence for bi-conditional representation ?

Select one:

a. ￢(p → q) ≡ p ∧￢q

b. p ↔ q ≡ (p ∧ q) ∨ (￢p ∧￢q)

c. p ↔ q ≡ ￢p ↔￢q)

d. All mentioned

The Correct answer is: ￢(p → q) ≡ p ∧￢q

Question:

By the second law of de-Morgan ￢(r ∨ s) is equivalent to

Select one:

a. ￢r ∧￢s

b. ￢(￢r ∨￢s)

c. ￢r ∨￢s

d. ￢r ∨ s

The Correct answer is: ￢r ∧￢s

Question:

Let P(x) be the statement “x + 1 > x.” For the real number domain, qualify the statement for truth value;

Select one:

a. ∀x∃P(x) is true

b. ∀xP(x) is true

c. ∃x∀P(x) is true

d. ∃xP(x) is true

The Correct answer is: ∀xP(x) is true

Question:

For {Z+: Z+ < 5} verify if ∀xP(x) holds good for P(x) is “x2 < 10”

Select one:

a. ∀xP(x) is a conjunction

b. None of these

c. ∀xP(x) is false

d. ∀xP(x) holds good

The Correct answer is: ∀xP(x) is false

Question:

Identify correct statement/s among the following

Select one:

a. The relation"Union of sets" is reflexive,but not symmetric

b. The relation"parallel of lines" is always an equivalence relation

c. The relation "Division" is Symmetric

The Correct answer is: The relation"parallel of lines" is always an equivalence relation

Question:

Which of the following is/are true ?

Select one or more:

a. p ∧￢p is always a contradiction

b. ￢p ∨ p is always a tautology

c. ￢p ∨ p is always a contradiction

d. p ∧￢p is always a tautology

The Correct answer is: ￢p ∨ p is always a tautology, p ∧￢p is always a contradiction

Question:

What of the following expressions does not imply the negation of the proposition, “there is an honest politician” if h(x) represents honesty function:

Select one:

a. ￢∃xH(x)

b. ∃xH(x)

c. ∀x￢H(x)

d. All of these

The Correct answer is: ∃xH(x)

Question:

“The sum of two positive integers is always positive” into a logical expression

Select one:

a. BOTH :∀x∀y((x > 0) ∧ (y > 0) → (x +y > 0)) and ∀x∀y(x +y > 0)

b. ∀x∀y((x > 0) ∧ (y > 0) → (x +y > 0))

c. Either ∀x∀y((x > 0) ∧ (y > 0) → (x +y > 0)) or ∀x∀y(x +y > 0)

d. ∀x∀y(x +y > 0)

The Correct answer is: BOTH :∀x∀y((x > 0) ∧ (y > 0) → (x +y > 0)) and ∀x∀y(x +y > 0)

Question:

Which of the following is/are statement/s

Select one or more:

a. How hot the day is

b. None of these are statements

c. The temperature is 40 degrees.

d. It is raining in the summer.

The Correct answer is: The temperature is 40 degrees., It is raining in the summer.

Question:

Let P be “you can take the flight,”

Let Q be “you buy a ticket.”

What of the following notates “you can take the flight if and only if you buy a ticket”

Select one:

a. None of these

b. Q → P

c. P → Q

d. P ↔ Q

The Correct answer is: P ↔ Q

August 26, 2019

Discrete Structures for Computer Science - MCQS

June 14, 2019

Discrete Structures for Computer Science - MCQS

𝐒𝐞𝐚𝐫𝐜𝐡 𝐓𝐡𝐢𝐬 𝐁𝐥𝐨𝐠

𝐅𝐀𝐂𝐄𝐁𝐎𝐎𝐊

𝐓𝐨𝐭𝐚𝐥 𝐒𝐜𝐡𝐨𝐥𝐚𝐫

𝕽𝖊𝖈𝖊𝖓𝖙

𝕱𝖊𝖆𝖙𝖚𝖗𝖊𝖉

Systems Programming- MCQS

𝐁𝐥𝐨𝐠 𝐀𝐫𝐜𝐡𝐢𝐯𝐞

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