×

Multiple-Choice Questions

Web Technologies MCQs

Computer Science Subjects MCQs

Databases MCQs

Programming MCQs

Testing Software MCQs

Digital Marketing Subjects MCQs

Cloud Computing Softwares MCQs

AI/ML Subjects MCQs

Engineering Subjects MCQs

Office Related Programs MCQs

Management MCQs

More

Discrete Mathematics | Mathematical Induction, Inclusion-Exclusion Principle and Binary Relation MCQs

Mathematical Induction, Inclusion-Exclusion Principle and Binary Relation MCQs: This section contains multiple-choice questions and answers on Mathematical Induction, Inclusion-Exclusion Principle and Binary Relation.
Submitted by Anushree Goswami, on July 10, 2022

1. Mathematical _____ establishes whether an ordinary result involving natural numbers is valid?

  1. Inflation
  2. Induction
  3. Intution
  4. Inhibition

Answer: B) Induction

Explanation:

Mathematical induction establishes whether an ordinary result involving natural numbers is valid.


2. P (n) is ___ for n = n0.?

  1. True
  2. False
  3. Not predictable
  4. None of the above

Answer: A) True

Explanation:

P (n) is true for n = n0.


3. If P (k) is true for n = k then -?

  1. P (K+1) must also be true
  2. P (n) is true for all n ≥ n0
  3. Both a and b
  4. None of the above

Answer: C) Both A and B

Explanation:

If P (k) is true for n = k then - i. P (K+1) must also be true ii. P (n) is true for all n ≥ n0


4. In Inclusion-Exlusion Principle, if A and B are any two finite sets then -?

  1. n (A ∩ B) = n (A) + n (B) - n (A ∩ B)
  2. n (A ∪ B) = n (A) + n (B) - n (A ∪ B)
  3. n (A ∪ B) = n (A) + n (B) - n (A ∩ B)
  4. n (A ∪ B) = n (A) + n (B) + n (A ∩ B)

Answer: C) n (A ∪ B) = n (A) + n (B) - n (A ∩ B)

Explanation:

In Inclusion-Exlusion Principle, if A and B are any two finite sets then n (A ∪ B) = n (A) + n (B) - n (A ∩ B).


5. Binary relations R are defined as subsets of P x Q from a set P to Q if P and Q are ____ sets?

  1. Empty
  2. Non-empty
  3. Half Empty
  4. None

Answer: B) Non-empty

Explanation:

Binary relations R are defined as subsets of P x Q from a set P to Q if P and Q are non-empty sets.


6. 24. A and B are related by the constant R if -?

  1. (a, b) ∈ R
  2. R ⊆ P x Q
  3. Both a and b
  4. None of the above

Answer: C) Both A and B

Explanation:

A and B are related by the constant R if (a, b) ∈ R and R ⊆ P x Q.


7. We say R ⊆ P x P is a relationship on P if P and Q are ____?

  1. Equivalent
  2. Non-equivalent
  3. Equal
  4. Non-equal

Answer: C) Equal

Explanation:

We say R ⊆ P x P is a relationship on P if P and Q are equal.


8.In relation R, the domain is all ____ entries of all pairs that relate some elements in P to some elements in Q.?

  1. First
  2. Second
  3. Third
  4. Last

Answer: A) First

Explanation:

In relation R, the domain is all first entries of all pairs that relate some elements in P to some elements in Q.


9.Domain of a relation is denoted by -?

  1. RAN (R)
  2. DOM (R)
  3. DAM (R)
  4. DOMA (R)

Answer: B) DOM (R)

Explanation:

Domain of a relation is denoted by DOM (R).


10.In R, the range is comprised of all ____ entries belonging to ordered pairs whose elements relate to some element in Q?

  1. First
  2. Second
  3. Third
  4. Last

Answer: B) Second

Explanation:

In R, the range is comprised of all second entries belonging to ordered pairs whose elements relate to some element in Q.


11.Range of a relation is denoted by -?

  1. RANGE (R)
  2. RAN (R)
  3. RANG (R)
  4. R (R)

Answer: B) RAN (R)

Explanation:

Range of a relation is denoted by RAN (R).


12.In case of complement of a relation -?

  1. R = {(a, b): {a, b) ∈ R}.
  2. R = {(a, b): {a, a) ∉ R}.
  3. R = {(a, b): {b, b) ∉ R}.
  4. R = {(a, b): {a, b) ∉ R}.

Answer: D) R = {(a, b): {a, b) ∉ R}.

Explanation:

In case of complement of a relation, R = {(a, b): {a, b) ∉ R}.





Comments and Discussions!

Load comments ↻





Copyright © 2024 www.includehelp.com. All rights reserved.