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Test: Discrete Mathematics - 2 - Computer Science Engineering (CSE) MCQ


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15 Questions MCQ Test GATE Computer Science Engineering(CSE) 2025 Mock Test Series - Test: Discrete Mathematics - 2

Test: Discrete Mathematics - 2 for Computer Science Engineering (CSE) 2024 is part of GATE Computer Science Engineering(CSE) 2025 Mock Test Series preparation. The Test: Discrete Mathematics - 2 questions and answers have been prepared according to the Computer Science Engineering (CSE) exam syllabus.The Test: Discrete Mathematics - 2 MCQs are made for Computer Science Engineering (CSE) 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Test: Discrete Mathematics - 2 below.
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Test: Discrete Mathematics - 2 - Question 1

Let P (x) denote the statement “x >7.” Which of these have truth value true?

Detailed Solution for Test: Discrete Mathematics - 2 - Question 1

Put x=9, 9>7 which is true.

Test: Discrete Mathematics - 2 - Question 2

The statement,” Every comedian is funny” where C(x) is “x is a comedian” and F (x) is “x is funny” and the domain consists of all people.

Detailed Solution for Test: Discrete Mathematics - 2 - Question 2

For every person x, if comedian then x is funny.

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Test: Discrete Mathematics - 2 - Question 3

”Everyone wants to learn cosmology.” This argument may be true for which domains?

Detailed Solution for Test: Discrete Mathematics - 2 - Question 3

Domain may be limited to your class or may be whole world both are good as it satisfies universal quantifier.

Test: Discrete Mathematics - 2 - Question 4

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

Detailed Solution for Test: Discrete Mathematics - 2 - Question 4

Statement is x is less than y. Quantifier used are for each x, there exists a y.

Test: Discrete Mathematics - 2 - Question 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.”

Detailed Solution for Test: Discrete Mathematics - 2 - Question 5

Joy is loved by all the people in the world.

Test: Discrete Mathematics - 2 - Question 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.

Detailed Solution for Test: Discrete Mathematics - 2 - Question 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. Correct Answer Amit does not like some dishes.

Negation of the statement Amit like South Indian dishes.

Test: Discrete Mathematics - 2 - Question 7

Which rule of inference is used in each of these arguments, “If it is Wednesday, then the Smartmart will be crowded. It is Wednesday. Thus, the Smartmart is crowded.”

Detailed Solution for Test: Discrete Mathematics - 2 - Question 7

(M ∧ (M → N)) → N is Modus ponens.

Test: Discrete Mathematics - 2 - Question 8

Which rule of inference is used in each of these arguments, “If it hailstoday, the local office will be closed. The local office is not closed today. Thus, it did not hailed today.”

Detailed Solution for Test: Discrete Mathematics - 2 - Question 8

(¬N ∧ (M → N)) → ¬M is Modus tollens.

Test: Discrete Mathematics - 2 - Question 9

What rule of inference is used here? “It is cloudy and drizzling now. Therefore, it is cloudy now.”

Detailed Solution for Test: Discrete Mathematics - 2 - Question 9

(p ∧ q) → p argument is Simplification.

Test: Discrete Mathematics - 2 - Question 10

What rules of inference are used in this argument? “All students in this science class has taken a course in physics” and “Marry is a student in this class” imply the conclusion “Marry has taken a course in physics.”

Detailed Solution for Test: Discrete Mathematics - 2 - Question 10

∀xP (x), ∴ P (c) Universal instantiation.

Test: Discrete Mathematics - 2 - Question 11

The premises (p ∧ q) ∨ r and r → s imply which of the conclusion?

Detailed Solution for Test: Discrete Mathematics - 2 - Question 11

The premises (p ∧ q) ∨ r has two clauses: p ∨ r, and q ∨ r.
We can also replace r → s with the equivalent clause r ∨ s.
Using the two clauses p ∨ r and r ∨ s, we can conclude p ∨ s.

Test: Discrete Mathematics - 2 - Question 12

“Parul is out for a trip or it is not snowing” and “It is snowing or Raju is playing chess” imply that __________

Detailed Solution for Test: Discrete Mathematics - 2 - Question 12

Let p be “It is snowing,” q be “Parul is out for a trip,” and r the proposition “Raju is playing chess.” The hypotheses as ¬p ∨ q and p ∨ r, respectively.
Using resolution, the proposition q ∨ r is, “Parul is out for a trip or Raju is playing chess.”

Test: Discrete Mathematics - 2 - Question 13

Which of the following can only be used in disproving the statements?

Detailed Solution for Test: Discrete Mathematics - 2 - Question 13

Counter examples cannot be used to prove results.

Test: Discrete Mathematics - 2 - Question 14

When to proof P→Q true, we proof P false, that type of proof is known as ___________

Detailed Solution for Test: Discrete Mathematics - 2 - Question 14

Definition of vacuous proof.

Test: Discrete Mathematics - 2 - Question 15

A proof covering all the possible cases, such type of proofs are known as

Detailed Solution for Test: Discrete Mathematics - 2 - Question 15

Definition of exhaustive proof.

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