Hello friends, in this post we are going to discuss about Discrete Structures for Computer Science Multiple choice question with answer | Discrete Structures for Computer Science Objective type question with answer | Discrete Structures for Computer Science Answer

## Q1.Let C(X) be the statement where X = X cube ,if domain consist of all integers then which one is correct from following

a. ⱯXC(X)

b. C(-1)

c. ƎXC(X)

d. C(0)

Ans: C

## Q2.Which of the following propositions is a tautology?

a. (p ˅ q) → q

b. p ˅ (q → p)

c. (p ˅ q) → p

d. p ˅ (p→q)

Ans: D

## Q3.’Every minor injury can be treated with turmeric.’ This statement is a _____

a. Proposition

b. Predicate

c. recurrence relation

d. inductive statement

Ans: D

## Q4.What rule of inference is used in the following argument?

*If it Monday, there will be no DSCS class. There is DSCS class today, Therefore, it is not Monday.*

a. Generalized Modus Ponens

b. Modus Ponens Incorrect

c. Addition

d. Modus Tollens

e. Resolution

Ans: D

## Q5.Which of the following statement is a proposition?

a. The only odd prime number is 2 Correct

b. God bless yu!

c. Get me glass of Milkshake

d. What is the time now?

Ans: A

## Q6.A proof that p → q is true based on the fact that q is true, such proofs are known as ___________

a. Proof by cases

b. Trivial proof Correct

c. Contrapositive proofs

d. Direct proof

Ans: B

## Q7.Value of X after the statement “if p(x) then x:=1” executed where P(x):x >1 and x = 0 when the statement reached:

a. 0

b. -1

c.1

d. 2

Ans: A

## Q8.(P^~p) and (pv~q) are

a. Tautology and contradiction respectively.

b. Both tautologies Incorrect

c. Contradiction and tautology respectively.

d. Both contradictions

Ans: C

## Q9.The statement form (p ⇔ r) ⇒ (q ⇔ r) is equivalent to

a. [(∼p ∨ r) ∧ (p ∨ ∼r)] ∨ ∼[(∼q ∨ r) ∧ (q ∨ ∼r)]

b. ∼ [(∼p ∨ r) ∧ (p ∨ ∼r)] ∧ [(∼q ∨ r) ∧ (q ∨ ∼r)]

c. ∼[(∼p ∨ r) ∧ (p ∨ ∼r)] ∧ [(∼q ∨ r) ∨ (q ∨ ∼r)]

d. [(∼p ∨ r) ∧ (p ∨ ∼r)] ∧ [(∼q ∨ r) ∧ (q ∨ ∼r)]

Ans: B

## Q10.Let P(n) be a statement that 1 + 1/4 + 1/9 + 1/16 + …. + 1/n^2, where n is an integer and greater than 1. Which of the following statements are true?

## 1.n > 1, ∀n belongs to N is true 2. P (2) is true 3. N=1 is true 4. N<2 is true

a. Only 1

b. All the statements are true

c. Both 3 and 4

d. Both 1 and 2

e. None of the statements are true

Ans: D

## Q11.Which of the following statements is the contrapositive of the statement, “You win the game if you know the rules but are not overconfident?”

a. A sufficient condition that you win the game is that you know the rules or you are not overconfident.

b. If you don’t know the rules or are overconfident you lose the game.

c. If you lose the game then you don’t know the rules or you are overconfident.

d. If you know the rules and are overconfident then you win the game

Ans: C

## Q12.Let P(x,y) denote the statement “ x+y is even”. Which of the following proposition has truth value “False”?

a. P(2,6)

b. P(0,0)

c. P(5,7)

d. P(1,4)

Ans: D

## Q13.Negation of the statement ‘Not everyone is mortal’ is…

a. Nobody is mortal

b. Someone is mortal.

c. Someone is immortal.

d. Everyone is immortal

Ans: D

## Q14.Using binary arithmetic, a number y is computed by taking the n-bit two’s complement of x − c. If n is eleven, x = 101000010012 and c = 101012 then y =

a. 011000000002

b. 011000111002

c. 011000011112

d. 011000011002

e. 010001111002

Ans: D

## Q15.Choose the correct option for the following argument:

`If I drive to work, then I will arrive tired.I arrive at work tired.`

\I drive to work.

a. Argument is valid and rule of inference used is modus ponens.

b. Argument is valid and rule of inference used is modus tollens.

c. Argument is valid and rule of inference used is Resolution.

d. Argument is not valid.

Ans: D

## Q16.Given the following conditional statements, determine the truth status and which is the match sequence choice

1) If tom is born on Feb 30th, then 3 + 4 = 8

2) If 1 + 1 = 3, then 2 + 2 = 4

3) If 1 + 1 = 2, then 2 + 2 = 5

**4) If 1 + 1 = 3, then 2 + 2 = 5**

a. T, T, F, T

b. T, T, F, F

c. F, F, T, F

d. T, T, T, T

e. F, F, T, T

Ans: A

## Q17.Name the rules of inference are used in the following argument? “Sushant is an awesome student. Sushant is also a good dancer. Therefore, Sushant is an awesome student and a good dancer.”

a. Simplification

b. Disjunctive syllogism

c. Modus ponens

d. Conjunction

Ans: D

## Q18.Which of the following is counterexample for the statement Ɐx, x + 3 > 7 where U = {3, 5, 7, 9}

a. 5

b. 9

c. 7

d. 3

Ans: D

## Q19.A → (A ∨ q) is a *__*_____

*__*

a. None of the above

b. Tautology

c. Contingency

d. Contradiction

Ans: B

## Q20.Let P: I am in Bombay.; Q: I love football.; then q -> p(q implies p) is?

a. I am not in Bombay

b. I love football

c. If I love football then I am in Bombay

d. If I am in Bombay then I love football

Ans: C