Paper 2 CS · UNIT 01 · MOCK TEST

Mock 4 – Mathematical Logic (Part 2)

Unit 1: Discrete Structures and Optimisation · 21 questions · about 25 minutes. Press End Mock any time to see your score and the correct answers.

All 14 topic-wise mocks in this unit

0 / 21 answered 00:00

Q1. The negation of "Some students like hockey" is:

ASome students dislike hockey BEvery student dislikes hockey CEvery student likes hockey DAll students like hockey

Q2. The logic expression (P′ ∧ Q) ∨ (P ∧ Q′) ∨ (P ∧ Q) is equivalent to

AP′ ∨ Q BP ∨ Q′ CP ∨ Q DP′ ∨ Q′

Q3. Consider α, β, γ as logical variables. Which of the following are correct logical equivalences?
(A) α ∧ (β ∨ γ) ≡ (α ∧ β) ∨ (α ∧ γ)
(B) α ∨ β ≡ ¬α ∨ β
(C) (α ⇒ β) ≡ (¬β ⇒ ¬α)
(D) ¬(α ∨ β) ≡ (¬α ⇒ ¬β)
Choose the correct answer from the options given below:

A(A) and (D) only B(B) and (C) only C(A) and (C) only D(B) and (D) only

Q4. Consider the following in Boolean algebra:
X: a ∨ (b ∧ (a ∨ c)) = (a ∨ b) ∧ (a ∨ c)
Y: a ∧ (b ∨ (a ∧ c)) = (a ∧ b) ∨ (a ∧ c)
The identity a ∨ (b ∧ c) = (a ∨ b) ∧ c is satisfied if

AX is true BY is true CBoth X and Y are true DIt does not depend on X and Y

Q5. Given below are two statements: Assertion (A) and Reason (R).
Assertion (A): ¬p
Reason (R): (r → ¬q, r ∨ s, s → ¬q, p → q)
In the light of the above statements, choose the correct answer.

ABoth (A) and (R) are true and (R) is the correct explanation of (A) BBoth (A) and (R) are true but (R) is NOT the correct explanation of (A) C(A) is true but (R) is false D(A) is false but (R) is true

Q6. The prototyping model has the sequence:
(A) Customer Evaluation
(B) Quick design
(C) Requirements
(D) Implement
(E) Design

A(C) → (A) → (D) → (B) → (E) B(B) → (C) → (A) → (D) → (E) C(C) → (B) → (D) → (A) → (E) D(E) → (B) → (C) → (D) → (A)

Q7. For the following set of processes scheduled using FCFS policy, determine the average waiting time. Assume that the processes arrived in the order P1, P2, P3, P4.

Process	Burst Time (ms)
P1	8
P2	15
P3	10
P4	7

A8 B16 C32 D48

Q8. Assuming that the system call fork() never fails, consider the following C programs P1 and P2 executed on a UNIX/Linux system.

P1	P2
int main() { fork(); fork(); fork(); printf("Happy\n"); }	int main() { fork(); printf("Happy\n"); fork(); printf("Happy\n"); fork(); printf("Happy\n"); }

Statement I: P1 displays "Happy" 8 times.
Statement II: P2 displays "Happy" 12 times.
In light of the above statements, choose the most appropriate answer.

ABoth Statement I and Statement II are true BBoth Statement I and Statement II are false CStatement I is correct but Statement II is false DStatement I is incorrect but Statement II is true

Q9.

Match List I with List II

List I List II

AA-II, B-I, C-IV, D-III BA-III, B-I, C-II, D-IV CA-IV, B-I, C-II, D-III DA-III, B-II, C-IV, D-I

Q10.

Match the logically equivalent propositions. List I: A. p → q, B. ¬(p ∨ (¬p ∧ q)), C. p ↔ q, D. ¬(p ↔ q). List II: I. (p ∧ q) ∨ (¬p ∧ ¬q), II. ¬p ∨ q, III. ¬(p ∨ q), IV. ¬p ↔ q.

AA-I, B-III, C-II, D-IV BA-I, B-II, C-III, D-IV CA-II, B-III, C-I, D-IV DA-II, B-III, C-IV, D-I

Q11.

Let P be "It is hot day" and q be "The temperature is 48°C". Write in simple sentences the meaning of ¬p∧¬q.

AIt is hot day or temperature is 48°C BIt is cold day or temperature is 48°C CIt is neither a hot day nor temperature is 48°C DIt is not a hot day

Q12.

If p and q are two statements, which of the following equivalences hold? (A) ~(p ∧ q) ≡ ~p ∨ ~q (B) ~(p ∨ q) ≡ ~p ∧ ~q (C) p ∧ ~p ≡ T (D) ~(p ⇒ q) ≡ p ∧ ~q (E) p ∨ q ≡ ~p ∨ ~q

A(A), (B) and (D) only B(A), (C) and (D) only C(C), (D) and (E) only D(A), (B) and (C) only

Q13.

Translate into English: ∀x ∃y (x < y), where the domain of both variables is the real numbers.

AFor all real numbers x, there exists a real number y such that x is less than y BFor every real numbers y, there exists a real number x such that x is less than y CFor some real numbers x, there exists a real number y such that x is less than y DFor each and every real numbers x and y, x is less than y

Q14.

Which of the following are true if the universe of discourse consists of all integers? A. ∀n∃m (n² < m) B. ∃n∀m (n < m²) C. ∃n∃m (n² + m² = 5) D. ∃n∃m (n² + m² = 6) E. ∃n∃m (m + n = 4 ∧ n − m = 1)

AA, B, C Only BB, C, E Only CC, D, E Only DB, D Only

Q15.

Match List - I with List - II.

AA-III, B-IV, C-II, D-I BA-III, B-IV, C-I, D-II CA-II, B-I, C-III, D-IV DA-II, B-I, C-IV, D-III

Q16.

Which of the following are tautologies? A. (p ∨ r) → p B. p → (p ∧ r) C. ~p → (p → r) D. (p ∧ r) → (p → r) E. ~(p → r) → p

AA, B Only BA, B, C Only CB, C, D Only DC, D, E Only

Directions (Q91–95): A firm produces two types of cloth, A and B, using red, green and blue wool. One unit length of type A needs 2 yards of red and 3 yards of green wool. One unit length of type B needs 3 yards of red, 2 yards of green and 2 yards of blue wool. The firm has 8 yards of red, 10 yards of green and 15 yards of blue wool. Income is ₹30 per unit length of type A and ₹50 per unit length of type B.

Q17.

On the basis of available material, maximum total income is :

A₹ 133.3 B₹ 124 C₹ 100 D₹ 153.3 Directions (96-100) Read the following passage and answer the given questions. A company is implementing a new database system to manage its customer information. The database contains labels for customers, orders, products and sales representatives. Each customer can place multiple orders and each order can contain multiple products. Each order is associated with a specific sales representative who manages the accountable products. The database is designed to improve efficiency in tracking sales and customer interactions.

Q18.

If the universe of discourse is all real numbers, which of the following are true? (A) ∃x∀y (x + y = y) (B) ∀x∀y (((x ≥ 0) ∧ (y < 0)) → (x − y > 0)) (C) ∃x∃y (((x ≤ 0) ∧ (y ≤ 0)) ∧ (x − y > 0)) (D) ∀x∀y (((x ≠ 0) ∧ (y ≠ 0)) ↔ (xy ≠ 0))

A(A) and (B) Only B(A), (C) and (D) Only C(A), (B) and (D) Only D(A), (B), (C) and (D) Only

Q19.

If the universe of discourse is the set of integers, which of the following are TRUE? (A) ∀n∃m (n² < m) (B) ∃n∀m (n < m²) (C) ∃n∀m (nm = m) (D) ∃n∃m (n² + m² = 6) (E) ∃n∃m (n + m = 4 ∧ n − m = 1)

A(A), (B) and (C) Only B(B) and (C) Only C(C), (D) and (E) Only D(C) and (E) Only

Q20.

Which of the following are tautology? → → → →

(A) (P (P Q)) (P Q) → → → ∨

(B) ((P Q) Q) (P Q) ∨¬ → → ∨¬ →

(D) (Q (P P)) (R (P P))

A(A) Only B(B) Only C(A) and(B) Only D(C) and (D) Only

Q21.

Let P(x) be the statement "x = x²". If the universe of discourse is the integers, which of the following are true? (A) P(0) (B) P(1) (C) P(2) (D) ∃x P(x) (E) ∀x P(x)

A(A), (B) and (E) Only B(A), (B) and (C) Only C(A), (B) and (D) Only D(B), (C) and (D) Only

Next: Mock 5 – Mathematical Logic (Part 3) →