## Discrete Mathematics MCQ Set 1

1. Let Q(x, y) denote “M + A = 0.” What is the truth value of the quantifications ∃A∀M Q(M, A)

a) True

b) False

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2. Translate ∀x∃y(x < y) in English, considering domain as real number for both the variable.

a) For all real number x there exists a real number y such that x is less than y

b) For every real number y there exists a real number x such that x is less than y

c) For some real number x there exists a real number y such that x is less than y

d) For each and every real number x and y such that x is less than y

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3. “The product of two negative real numbers is not negative.” Is given by?

a) ∃x ∀y ((x < 0) ∧ (y < 0) → (xy > 0))

b) ∃x ∃y ((x < 0) ∧ (y < 0) ∧ (xy > 0))

c) ∀x ∃y ((x < 0) ∧ (y < 0) ∧ (xy > 0))

d) ∀x ∀y ((x < 0) ∧ (y < 0) → (xy > 0))

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4. Let Q(x, y) be the statement “x + y = x − y.” If the domain for both variables consists of all integers, what is the truth value of ∃xQ(x, 4).

a) True

b) False

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5. Let L(x, y) be the statement “x loves y,” where the domain for both x and y consists of all people in the world.

Use quantifiers to express , “Joy is loved by everyone.”

a) ∀x L(x, Joy)

b) ∀y L(Joy,y)

c) ∃y∀x L(x, y)

d) ∃x ¬L(Joy, x)

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6. Let T (x, y) mean that student x likes dish y, where the domain for x consists of all students at your school and the domain for y consists of all dishes. Express ¬T (Amit, South Indian) by a simple English sentence.

a) All students does not like South Indian dishes.

b) Amit does not like South Indian people.

c) Amit does not like South Indian dishes.

d) Amit does not like some dishes.

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7. Express, “The difference of a real number and itself is zero” using required operators.

a) ∀x(x − x! = 0)

b) ∀x(x − x = 0)

c) ∀x∀y(x − y = 0)

d) ∃x(x − x = 0)

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8. Use quantifiers and predicates with more than one variable to express, “There is a pupil in this lecture who has taken at least one course in Discrete Maths.”

a) ∃x∃yP (x, y), where P (x, y) is “x has taken y,” the domain for x consists of all pupil in this class, and the domain for y consists of all Discrete Maths lectures

b) ∃x∃yP (x, y), where P (x, y) is “x has taken y,” the domain for x consists of all Discrete Maths lectures, and the domain for y consists of all pupil in this class

c) ∀x∀yP(x, y), where P (x, y) is “x has taken y,” the domain for x consists of all pupil in this class, and the domain for y consists of all Discrete Maths lectures

d) ∃x∀yP(x, y), where P (x, y) is “x has taken y,” the domain for x consists of all pupil in this class, and the domain for y consists of all Discrete Maths lectures

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9. Determine the truth value of ∃n∃m(n + m = 5 ∧ n − m = 2) if the domain for all variables consists of all integers.

a) True

b) False

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10. Find a counterexample of ∀x∀y(xy > y), where the domain for all variables consists of all integers.

a) x = -1, y = 17

b) x = -2 y = 8

c) Both a and b

d) Does not have any counter example

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## Discrete Mathematics MCQ Set 2

1. If there exist an integer x such that x^{2} ≡ q (mod n). then q is called:

a) Quadratic Residue

b) Linear Residue

c) Pseudoprime

d) None of the mentioned

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2. If there exist no integer x such that x^{2} ≡ q (mod n). then q is called:

a) Quadratic Residue

b) Quadratic Nonresidue

c) Pseudoprime

d) None of the mentioned

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3. The Fermat’s little theorem for odd prime p and coprime number a,is:

a) a^{p-1} ≡ 1 (mod p)

b) a^{p-1} ≡ 7 (mod p)

c) a^{p(2)-1} ≡ 1 (mod p)

d) None of the mentioned

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^{p-1}≡ 1 (mod p).

4. State whether the given statement is true or false

5 is quardratic non-residue of 7.

a) True

b) False

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5. State whether the given statement is true or false

4 is quardratic residue of 7.

a) True

b) False

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6. State whether the given statement is true or false

8 is quardratic residue of 17.

a) True

b) False

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7. State whether the given statement is true or false

8 is quardratic residue of 11 .

a) True

b) False

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^{2}≡ 8(mod)17 has no solutions.

8. Which of the following is a quardratic residue of 11?

a) 4

b) 5

c) 9

d) All of the mentioned

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9. A pseudo prime number is

a) is a probable prime and is not a prime number

b) is a prime number

c) does not share any property with prime number

d) none of the mentioned

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10. Pseudo prime are classified based on property which they satisfy,which of the following are classes of pseudoprimes:

a) Fermat pseudoprime

b) Fibonacci pseudoprime

c) Euler pseudoprime

d) All of the mentioned

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## Discrete Mathematics MCQ Set 3

1. Let A and B be two matrices of same order ,then state whether the given statement is true or false:

A + B = B + A

a) True

b) False

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2. Let A and B be two matrices of same order, then state whether the given statement is true or false:

AB = BA

a) True

b) False

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3. Let A order(axb) and Border(cxd) be two matrices, then for AB to exist, correct relation is given by:

a) a = d

b) b = c

c) a = b

d) c = d

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4. Let A order(axb) and Border(cxd) be two matrices, then if AB exists, the order of AB is:

a) axd

b) bxc

c) axb

d) cxd

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5. Let A=[a_{ij} ] be an mxn matrix and k be a scalar then kA is equal to :

a) [ka_{ij} ]_{mxn}

b) [a_{ij}/k ]_{mxn}

c) [k^{2} a_{ij} ]_{mxn}

d) None of the mentioned

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6. State True or False:

The matrix multiplication is distrbutive over matrix addition.

a) True

b) False

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7. If for a square matrix A, A^{2} = A then such a matrix is known as:

a) Idempotent matrix

b) Orthagonal matrix

c) Null matrix

d) None of the mentioned

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^{2}= A.

8. State whether the given statement is True or False.

For matrix A, B.(A+B)^{T} = A^{T} + B^{T} and (AB)^{T} = A^{T}B^{T} if the orders of matrices are appropriate.

a) True

b) False

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^{T}= A

^{T}+ B

^{T}is correct but (AB)

^{T}= B

^{T}A

^{T}(reversal law).

9. For matrix A, B if A – B = O, where O is a null matrix then

a) A = O

b) B = O

c) A = B

d) None of the mentioned

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10. All the diagonal elements of a skew-symmetric matrix is:

a) 0

b) 1

c) 2

d) Any integer

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_{ij}= -a

_{ij}, this implies all diagonal elements should be zero.

## Discrete Mathematics MCQ Set 4

1. The number of factors of a prime numbers are:

a) 2

b) 3

c) Depends on the prime number

d) None of the mentioned

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2. The number ‘ 1’ is :

a) Prime number

b) Composite number

c) Neither Prime nor Composite

d) None of the mentioned

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3. State whether True or False

All prime numbers are odd.

a) True

b) False

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4. State whether True or False

3 is the smallest prime number possible.

a) True

b) False

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5. How may prime numbers are there between 1 to 20.

a) 5

b) 6

c) 7

4) None of the mentioned

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6. State whether the given statement is true or false

There are finite number of prime numbers.

a) True

b) False

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7. Sum of two different prime number is a:

a) Prime number

b) Composite number

c) Either Prime or Composite

d) None of the mentioned

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8. Difference of two distinct prime numbers is ?

a) Odd and prime

b) Even and composite

c) None of the mentioned

d) All of the mentioned

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9. If a, b, c, d are distinct prime numbers with a as smallest prime then a * b * c * d is a:

a) Odd number

b) Even number

c) Prime number

d) None of the mentioned.

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10. If a, b are two distinct prime number than highest common factor of a, b is

a) 2

b) 0

c) 1

d) ab

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## Discrete Mathematics MCQ Set 5

1. The determinant of identity matrix is :

a) 1

b) 0

c) Depends on the matrix

d) None of the mentioned

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_{ii}= 1, and all other elements = 0, hence the determinant is 1.

2. If determinant of a matrix A is Zero than:

a) A is a Singular matrix

b) A is a non-Singular matrix

c) Can’t say

d) None of the mentioned

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3. For a skew symmetric even ordered matrix A of integers, which of the following will not hold true:

a) det(A) = 9

b) det(A) = 81

c) det(A) = 7

d) det(A) = 4

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4. For a skew symmetric odd ordered matrix A of integers, which of the following will hold true:

a) det(A) = 9

b) det(A) = 81

c) det(A) = 0

d) det(A) = 4

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5. Let A = [ka_{ij} ]_{nxn}, B = [a_{ij} ]_{nxn}, be an nxn matrices and k be a scalar then det(A) is equal to:

a) Kdet(B)

b) K^{n}det(B)

c) K^{3}det(b)

4) None of the mentioned

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^{n}det(B).

6. State True or False:

The Inverse exist only for non-singular matrices.

a) True

b) False

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7. State True or False:

If for a square matrix A and B,null matrix O, AB =O implies BA=O:

a) True

b) False

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8. State whether the given statement is True or False.

If for a square matrix A and B,null matrix O, AB =O implies A=O and B=O.

a) True

b) False

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9. Let A be a nilpotent matrix of order n then

a) A^{n} = O

b) nA = O

c) A = nI, I is Identity matrix

d) None of the mentioned

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10. Which of the following property of matrix multiplication is correct:

a) Multiplication is not commutative in genral

b) Multiplication is associative

c) Multiplication is distributive over addition

d) All of the mentioned