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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.

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2. P (n) is ___ for n = n_0.?

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

Answer: A) True

Explanation:

P (n) is true for n = n_0.

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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

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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).

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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.

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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.

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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.

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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.

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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).

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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.

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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).

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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}.

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