Discrete Structures for Computer Science Multiple choice question | Discrete Structures for Computer Science Objective type question with answer | Discrete Structures for Computer Science Answer | Discrete Structures for Computer Science Dumps

## Q21.Let **A** be a set containing all upper and lower case English alphabets. Let **R** be a relation defined on **A × A**. The relation **R** consisting ordered pair (*x*, *y*) such that *x* and *y* should be same alphabet and that alphabet can be of same case or different case. Check which relation property does **R** satisfies.

a. Only reflexive

b. Both reflexive and symmetric

c. Only transitive

d. Reflexive, symmetric and transitive

Ans: d

## Q22.The recurrence relation for the sequence 1, 1, 2, 3, 5, …… is

a. fn= f n-1+ f n-2 and the initial conditions f0= 0 and f1= 1

b. fn= 2f n-1- f n-2 and the initial conditions f0= 0 and f1= 1

c. fn= f n-1+ f n-2 and the initial conditions f0= 1 and f1= 1

d. fn= 2fn-1 – f n-2 and the initial conditions f0= 1 and f1= 1

Ans: C

## Q23.Set A has 4 elements and set B has 3 elements then number of injections defined from B to A are?

a. 48

b. 12

c. 24

d. 36

Ans: C

## Q24.Let A = Z+, be the set of positive integers, and R be the relation on A defined by a R b if and only if there exist a k ∈Z+ such that a = bk. Which one of the following belongs to R?

a. (16, 256)

b. (169, 13)

c. (8, 128)

d. (11, 3)

Ans: B

## Q25.f : [0,π] →R given by f(x) = sinx is

a. not one to one

b. one to one function

c. bijective function

d. onto function

Ans: A

## Q26.Which of the following is a valid argument?

a. If I have a fever, then I go to the nurse. I don’t have a fever. Therefore, I went to the nurse

b. If I have a fever, then I go to the nurse. I didn’t go to the nurse. Therefore, I have a fever.

c. If I have a fever, then I go to the nurse. I have a fever. Therefore, I didn’t go to the nurse.

d. If I have a fever, then I go to the nurse. I didn’t go to the nurse. Therefore, I don’t have a fever

Ans: D

## Q27.Ramesh is out for a picnic or it is not raining” and “It is raining or Rakesh is playing carom” imply that *__*

*__*

a. Ramesh is out for a picnic and Rakesh is playing carom

b. Rakesh is playing carom

c. Ramesh is out for picnic

d. Ramesh is out for a picnic or Rakesh is playing carom

Ans: D

## Q28.If A, B and C are subsets of the universal set of all natural numbers. Then (A – C) ∩ (C – B) is

a. A ∩ B

b. A

c. Ø

d. C

Ans: C

## Q29.Find the correction option in perspective of given statements (i) Strictly increasing function from R to itself is one-to-one. (ii) Strictly decreasing function from R to itself is one-to-one.

a. Both (i) and (ii) are true.

b. (i) is true but (ii) is false

c. Both (i) and (ii) are false

d. (ii) is true but (i) is false

Ans: A

## Q30.If aRb → bRa, then the relation R is said to be

a. asymmetric

b. anti-symmetric

c. symmetric

d. none

Ans: C

## Q31.Which rule of inference is used in each of these arguments, “If it is Monday, then the roads will be crowded. It is Monday. Thus, the roads are crowded.”

a. Modus tollens

b. Disjunctive syllogism

c. Simplification

d. Modus ponens

Ans: D

## Q32.Let T be a set containing all the teachers of the university, M is a subset of T containing all teachers who teach Mathematics. C is also a subset of T containing all teachers who teach Computer Science. There are teachers who teach both Mathematics and Computer Science. Which of the following set operation shall list down all the teachers who teach either Mathematics or Computer Science and not both?

a. M ⊕ T

b. M – T

c. M ∩ T

d. T – M

Ans: A

## Q33.Which of the following is the Poset.

a. (R, ≠)

b. (R, ≥)

c. (R, =)

d. (R, <)

Ans: B

## Q34.Data stored on a computer disk or transmitted over a data network are represented as a string of bytes. How many bytes are required to encode 500 bits of data?

a. 60 bytes

b. 61 bytes

c. 62 bytes

d. 63 bytes

Ans: D

## Q35.From the set of premises given below, Identify the relevant conclusion can be drawn using rules of inference? If I work whole night on this homework, then I can answer all the exercises. If I answer all the exercises, I will understand the material.

a. If I work all night on this homework, then I will not understand the material

b. If I do not understand the material then I will not work all night on this homework

c. If I do not work all night on this homework, then I will understand the material

d. If I do not work all night on this homework, then I will not understand the material

Ans: B

## Q36.Consider the following arguments “If it is Thursday, then the Jio mart will be rush Jio mart is not rush. Therefore, it is not Thursday.” Which rule of inference is used in each of these arguments

a. Simplification

b. Modus ponens

c. Disjunctive syllogism

d. Modus tollens

Ans: D

## Q37.If f is a function on a set A= {2,3,4} such that f= { (2,2),(3,3),(4,4)}. Then

a. f is bijective

b. f is bijective but not surjective

c. None of the above

d. f is surjective but not injective

Ans: A

## Q38.A relation is symmetric if, we observe that for all values of a and b:

a. a R a

b. All the above

c. a=b

d. a R b implies b R a

Ans: D

## Q39.Which of these pairs of elements are incomparable in the Poset (Z+,|)?

a. 7,7

b. 6,18

c. 5,15

d. 6,9

Ans: D

## Q40.Let R1 = {(1,3), (2,1), (2,3), (3,1), (3,2)} and R2 = {(1,2), (1,3), (2,3)} R1⊕R2 is *_____________*

*_____________*a. {(2,1), (3,1), (3,2)}

b. {(1,2), (1,3), (2,1), (2,3), (3,1), (3,2)}

c. {(1,3), (2,3)}

d. {(1,2), (2,1), (3,1), (3,2)}

Ans: D