# Discrete Mathematics Questions and Answers – Logics – Inference

This set of Discrete Mathematics Multiple Choice Questions & Answers (MCQs) focuses on “Logics – Inference”.

1. 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.”
a) Modus tollens
b) Modus ponens
c) Disjunctive syllogism
d) Simplification

Explanation: (M ∧ (M → N)) → N is Modus ponens.

2. 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

Explanation: (¬N ∧ (M → N)) → ¬M is Modus tollens.

3. 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
d) Disjunctive syllogism

Explanation: p → (p ∨ q) argument is ‘Addition’.

4. What rule of inference is used here?
“It is cloudy and drizzling now. Therefore, it is cloudy now.”
b) Simplification
c) Resolution
d) Conjunction

Explanation: (p ∧ q) → p argument is Simplification.

5. 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

Explanation: ((p → q) ∧ (q → r)) → (p → r) argument is ‘Hypothetical syllogism’.
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6. 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

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

7. 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

Explanation: ((p ∨ q) ∧ ¬p) → q argument is Disjunctive syllogism.

8. 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

Explanation: 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.

9. 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

Explanation: ((p) ∧ (q)) → (p ∧ q) argument is conjunction.

10. “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

Explanation: 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.”

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