## Discrete Mathematics MCQ Set 1

1. Which of the following statements is the negation of the statements “4 is odd or -9 is positive”?

a) 4 is even or -9 is not negative

b) 4 is odd or -9 is not negative

c) 4 is even and -9 is negative

d) 4 is odd and -9 is not negative

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2. Which of the following represents: ~A (negation of A) if A stands for “I like badminton but hate maths”?

a) I hate badminton and maths

b) I do not like badminton or maths

c) I dislike badminton but love maths

d) I hate badminton or like maths

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3. The compound statement A v ~(A ∧ B) is always

a) True

b) False

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4. Which of the following are De-Morgan’s law

1) P ∧ (Q v R) Ξ ( P ∧ Q ) v ( P ∧ R )

2) ~(P ∧ R) Ξ ~P v ~R , ~(P v R) Ξ ~P ∧ ~R

3) P v ~P Ξ True , P ∧ ~P Ξ False

4) None of the mentioned

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5. What is the dual of (A ∧ B) v ( C ∧ D) ?

a) (A V B) v ( C v D)

b) (A V B) ^ ( C v D)

c) (A V B) v ( C ∧ D)

d) (A ∧ B) v ( C v D)

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6. ~ A v ~ B is logically equivalent to

a) ~ A → ~ B

b) ~ A ∧ ~ B

c) A → ~B

d) B V A

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7. Negation of statement (A ∧ B) → (B ∧ C)

a) (A ∧ B) →(~B ∧ ~C)

b) ~(A ∧ B) v ( B v C)

c) ~(A →B) →(~B ∧ C)

d) None of the mentioned

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8. Which of the following satisfies commutative law?

a) ∧

b) v

c) <->

d) All of the mentioned

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9. If the truth value of A v B is true, then truth value of ~A ∧ B can be

a) True if A is false

b) False if A is false

c) False if B is true and A is false

d) None of the mentioned

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10. If P is always against the testimony of Q ,then the compound statement P→(P v ~Q) is a

a) Tautology

b) Contradiction

c) Contingency

d) None of the mentioned

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## Discrete Mathematics MCQ Set 2

1. For an inverse to exist it is necessary that a function should be :

a) injection

b) bijection

c) surjection

d) none of the mentioned

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2. If f(x) = y then f ^{-1}(y) is equal to :

a) y

b) x

c) x^{2}

d) none of the mentioned

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^{-1}(y) = x.

3. A function f(x) is defined from A to B then f ^{-1} is defined :

a) from A to B

b) from B to A

c) depends on the inverse of function

d) none of the mentioned

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4. If f is a function defined from R to R , is given by f(x) = 3x – 5 then f ^{–1}(x) is given by:

a) 1/(3x-5)

b) (x+5)/3

c) does not exist since it is not a bijection

d) none of the mentioned

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^{-1}(x) = (x+5)/3.

5. State whether the given statement is true or false

For some bijective function inverse of that function is not bijective.

a) True

b) False

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^{-1}(x) is also a bijection.

6. State whether the given statement is true or false

f(x) is a bijection than f ^{-1}(x) is a mirror image of f(x) around y = x.

a) True

b) False

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7. If f is a function defined from R to R , is given by f(x) = x^{2} then f ^{–1}(x) is given by:

a) 1/(3x-5)

b) (x+5)/3

c) does not exist since it is not a bijection

d) none of the mentioned

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8. For any function fof ^{-1}(x) is equal to ?

a) x

b) 1

c) x^{2}

d) none of the mentioned

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9. The solution to f(x) = f ^{-1}(x) are :

a) no solutions in any case

b) same as solution to f(x) = x

c) infinite number of solution for every case

d) none of the mentioned

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10. State True or False.

Let f(x) = x then number of solution to f(x) = f ^{-1}(x) is zero.

a) True

b) False

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## Discrete Mathematics MCQ Set 3

1. A compound proposition that is always ___________ is called a tautology.

a) True

b) False

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2. A compound proposition that is always ___________ is called a contradiction.

a) True

b) False

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3. If A is any statement, then which of the following is a tautology?

a) A ∧ F

b) A ∨ F

c) A ∨ ¬A

d) A ∧ T

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4. If A is any statement, then which of the following is not a contradiction?

a) A ∨ ¬A

b) A ∨ F

c) A ∧ F

d) None of mentioned.

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5. A compound proposition that is neither a tautology nor a contradiction is called a ___________

a) Contingency

b) Equivalence

c) Condition

d) Inference

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6. ¬ (A ∨ q) ∧ (A ∧ q) is a ___________

a) Tautology

b) Contradiction

c) Contingency

d) None of the mentioned

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7. (A ∨ ¬A) ∨ (q ∨ T) is a __________

a) Tautology

b) Contradiction

c) Contingency

d) None of the mentioned

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8. A ∧ ¬(A ∨ (A ∧ T)) is always __________

a) True

b) False

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9. (A ∨ F) ∨ (A ∨ T) is always _________

a) True

b) False

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10. A → (A ∨ q) is a __________

a) Tautology

b) Contradiction

c) Contingency

d) None of the mentioned

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## Discrete Mathematics MCQ Set 4

1. A floor function map a real number to :

a) smallest previous integer

b) greatest previous integer

c) smallest following integer

d) none of the mentioned

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2. A ceil function map a real number to :

a) smallest previous integer

b) greatest previous integer

c) smallest following integer

d) none of the mentioned

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3. A function f(x) is defined as f(x) = x – [x], where [.] represents GIF then:

a) f(x) will be intergral part of x

b) f(x) will be fractional part of x

c) f(x) will always be 0

d) none of the mentioned

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4. Floor(2.4) + Ceil(2.9) is equal to :

a) 4

b) 6

c) 5

d) none of the mentioned

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5. State whether the given statement is true or false

For some integer n such that x < n < x + 1, ceil(x) < n .

a) True

b) False

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6. State whether the given statement is true or false

For some number x, Floor(x) <= x <= Ceil(x).

a) True

b) False

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7. If x, and y are positive numbers both are less than one, then maximum value of floor(x + y) is?

a) 0

b) 1

c) 2

d) -1

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8. If x, and y are positive numbers both are less than one ,then maximum value of ceil(x + y) is?

a) 0

b) 1

c) 2

d) -1

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9. If X = Floor(X) = Ceil(X) then :

a) X is a fractional number

b) X is a Integer

c) X is less than 1

d) none of the mentioned

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10.State True or False.

Let n be some integer greater than 1,then floor((n-1)/n) is 1.

a) True

b) False

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## Discrete Mathematics MCQ Set 5

1. To measure Time complexity of an algorithm Big O notation is used which:

a) describes limiting behaviour of the function

b) characterises a function based on growth of function

c) upper bound on growth rate of the function

d) all of the mentioned

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2. If for an algorithm time complexity is given by O(1) then complexityof it is:

a) constant

b) polynomial

c) exponential

d) none of the mentioned

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3. If for an algorithm time complexity is given by O(log_{2}n) then complexity will:

a) constant

b) polynomial

c) exponential

d) none of the mentioned

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4. If for an algorithm time complexity is given by O(n) then complexityof it is:

a) constant

b) linear

c) exponential

d) none of the mentioned

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5. If for an algorithm time complexity is given by O(n^{2}) then complexity will:

a) constant

b) quardratic

c) exponential

d) none of the mentioned

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6. If for an algorithm time complexity is given by O((^{3}⁄_{2})^{n}) then complexity will:

a) constant

b) quardratic

c) exponential

d) none of the mentioned

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7. The time complexity of binary search is given by:

a) constant

b) quardratic

c) exponential

d) none of the mentioned

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_{2}n), therefore complexity will be logarithmic.

8. The time complexity of linear search is given by:

a) O(log_{2}n)

b) O(1)

c) exponential

d) none of the mentioned

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9. Which algorithm is better for sorting between bubble sort and quicksort?

a) bubble sort

b) quick sort

c) both are equally good

d) none of the mentioned

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10. State true or false

Time complexity of binary search algorithm is constant.

a) True

b) False

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_{2}n), therefore complexity will be logarithmic.