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Welcome to the Logics and Proofs MCQs Page

Dive deep into the fascinating world of Logics and Proofs with our comprehensive set of Multiple-Choice Questions (MCQs). This page is dedicated to exploring the fundamental concepts and intricacies of Logics and Proofs, a crucial aspect of Discrete Mathematics. In this section, you will encounter a diverse range of MCQs that cover various aspects of Logics and Proofs, from the basic principles to advanced topics. Each question is thoughtfully crafted to challenge your knowledge and deepen your understanding of this critical subcategory within Discrete Mathematics.

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Check out the MCQs below to embark on an enriching journey through Logics and Proofs. Test your knowledge, expand your horizons, and solidify your grasp on this vital area of Discrete Mathematics.

Note: Each MCQ comes with multiple answer choices. Select the most appropriate option and test your understanding of Logics and Proofs. You can click on an option to test your knowledge before viewing the solution for a MCQ. Happy learning!

Logics and Proofs MCQs | Page 11 of 12

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Q101.
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.”

a.

Modus tollens

b.

Conjunction

c.

Hypothetical syllogism

d.

Simplification

Discuss
Answer: (a).Modus tollens
Q102.
Which rule of inference is used, ”Bhavika will work in an enterprise this summer. Therefore, this summer Bhavika will work in an enterprise or he will go to beach.”

a.

Simplification

b.

Conjunction

c.

Addition

d.

Disjunctive syllogism

Discuss
Answer: (c).Addition
Q103.
What rule of inference is used here?

“It is cloudy and drizzling now. Therefore, it is cloudy now.”

a.

Addition

b.

Simplification

c.

Resolution

d.

Conjunction

Discuss
Answer: (b).Simplification
Q104.
What rule of inference is used in this argument?

“If I go for a balanced diet, then I will be fit. If I will be fit, then I will remain healthy. Therefore, if I go for a balanced diet, then I will remain healthy.”

a.

Modus tollens

b.

Modus ponens

c.

Disjunctive syllogism

d.

Hypothetical syllogism

Discuss
Answer: (d).Hypothetical syllogism
Q105.
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.”

a.

Universal instantiation

b.

Universal generalization

c.

Existential instantiation

d.

Existential generalization

Discuss
Answer: (a).Universal instantiation
Q106.
What rules of inference are used in this argument?

“It is either colder than Himalaya today or the pollution is harmful. It is hotter than Himalaya today. Therefore, the pollution is harmful.”

a.

Conjunction

b.

Modus ponens

c.

Disjunctive syllogism

d.

Hypothetical syllogism

Discuss
Answer: (c).Disjunctive syllogism
Q107.
The premises (p ∧ q) ∨ r and r → s imply which of the conclusion?

a.

p ∨ r

b.

p ∨ s

c.

p ∨ q

d.

q ∨ r

Discuss
Answer: (b).p ∨ s
Q108.
What rules of inference are used in this argument?

“Jay is an awesome student. Jay is also a good dancer. Therefore, Jay is an awesome student and a good dancer.”

a.

Conjunction

b.

Modus ponens

c.

Disjunctive syllogism

d.

Simplification

Discuss
Answer: (a).Conjunction
Q109.
“Parul is out for a trip or it is not snowing” and “It is snowing or Raju is playing chess” imply that __________

a.

Parul is out for trip

b.

Raju is playing chess

c.

Parul is out for a trip and Raju is playing chess

d.

Parul is out for a trip or Raju is playing chess

Discuss
Answer: (d).Parul is out for a trip or Raju is playing chess
Q110.
Let the statement be “If n is not an odd integer then square of n is not odd.”, then if P(n) is “n is an not an odd integer” and Q(n) is “(square of n) is not odd.” For direct proof we should prove _________

a.

∀nP ((n) → Q(n))

b.

∃ nP ((n) → Q(n))

c.

∀n~(P ((n)) → Q(n))

d.

∀nP ((n) → ~(Q(n)))

Discuss
Answer: (a).∀nP ((n) → Q(n))
Page 11 of 12

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