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Discrete Mathematics | Predicate Logics MCQs

Discrete Mathematics | Predicate Logics MCQs: This section contains multiple-choice questions and answers on Predicate Logics in Discrete Mathematics.
Submitted by Anushree Goswami, on July 18, 2022

1. A predicate is a proposition containing ____, which is what's dealt with in predicate logic?

1. Statics
2. Variables
3. Numbers
4. None

Answer: B) Variables

Explanation:

A predicate is a proposition containing variables, which is what's dealt with in predicate logic.

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2. Predicates represent one or more variables that are determined on a specific ____?

1. Domain
2. Co-domain
3. Both a and b
4. None of the above

Answer: A) Domain

Explanation:

Predicates represent one or more variables that are determined on a specific domain.

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3. By ______, a predicate with variables can be made into a proposition?

1. Authorizing a value to a variable
2. Quantifying variable
3. Both A and B
4. None of the above

Answer: C) Both A and B

Explanation:

By authorizing a value to a variable or by quantifying it, a predicate with variables can be made into a proposition.

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4. A ____ quantifies a variable of a predicate?

1. Proposition
2. Quantity
3. Quality
4. Quantifier

Answer: D) Quantifier

Explanation:

A quantifier quantifies a variable of a predicate.

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5. How many types of quantifier are there in predicate logic?

1. 2
2. 3
3. 4
4. 5

Answer: A) 2

Explanation:

There are 2 types of quantifier in predicate logic.

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6. Which of the following is/are the type(s) of quantifier in predicate logic?

1. Existential
2. Universal
3. Both A and B
4. None of the above

Answer: C) Both A and B

Explanation:

The types of quantifier in predicate logic are -

1. Existential
2. Universal

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7. In case of existential quantifer, the proposition p(x) over the universe U is denoted by ____?

1. x∃p(x)
2. p(x)∃x
3. p(x)x∃
4. ∃x p(x)

Answer: D) ∃x p(x)

Explanation:

In case of existential quantifier, the proposition p(x) over the universe U is denoted by ∃x p(x).

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8. ∃x p(x) is read as -?

1. There exists one value in the universe of variable x such that p(x) is true
2. There exists at least one value in the universe of variable x such that p(x) is false
3. There exists at least one value in the universe of variable p(x) such that x is true
4. There exists at least one value in the universe of variable x such that p(x) is true

Answer: D) There exists at least one value in the universe of variable x such that p(x) is true

Explanation:

∃x p(x) is read as “There exists at least one value in the universe of variable x such that p(x) is true”.

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9. Quantifier ∃ is called _____ quantifier?

1. Existential
2. Universal
3. Both A and B
4. None of the above

Answer: A) Existential

Explanation:

Quantifier ∃ is called existential quantifier.

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10. An existential quantifier can be written in which way(s) in a proposition -?

1. (∃x∈A)p(x)
2. ∃x∈A such that p (x)
3. (∃x)p(x)
4. All of the above

Answer: D) All of the above

Explanation:

An existential quantifier can be used in several ways in a proposition -

1. (∃x∈A)p(x)
2. ∃x∈A such that p (x)
3. (∃x)p(x)

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11. In case of universal quantifer, the proposition p(x) over the universe U is denoted by ____?

1. x∀p(x)
2. p(x),∃∀
3. p(x),x∀
4. ∀x,p(x)

Answer: D) ∀x,p(x)

Explanation:

In case of universal quantifier, the proposition p(x) over the universe U is denoted by ∀x,p(x).

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12. ∀x,p(x) is read as -?

1. For every x∈U,p(x) isfalse
2. For every x∈p(x) is true
3. For every x∈U,p(x) is true
4. For every p(x) is true

Answer: C) For every x∈U,p(x) is true

Explanation:

∀x,p(x) is read as for every x∈U,p(x) is true.

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13. Quantifier ∀ is called ____ quantifier?

1. Existential
2. Universal
3. Both A and B
4. None of the above

Answer: B) Universal

Explanation:

Quantifier ∀ is called universal quantifier.

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14. An universal quantifier can be written in which way(s) in a proposition -?

1. ∀x∈A,p(x)
2. p(x), ∀x ∈A
3. ∀x,p(x)
4. All of the above

Answer: D) All of the above

Explanation:

An universal quantifier can be used in several ways in a proposition -

1. ∀x∈A,p(x)
2. p(x), ∀x ∈A
3. ∀x,p(x)

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15. Which of the following statement is/are TRUE?

1. An existentially quantified proposition arises from negating a universally quantified proposition
2. An universally quantified proposition arises from negating a existentially quantified proposition
3. Both A and B
4. None of the above

Answer: C) Both A and B

Explanation:

The following statement is TRUE -

1. An existentially quantified proposition arises from negating a universally quantified proposition
2. An universally quantified proposition arises from negating a existentially quantified proposition

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16. What is the rule for the negation of quantified proposition?

1. Dissociative law
2. Associative law
3. Demorgan’s law
4. Identity law

Answer: C) Demorgan's law

Explanation:

Demorgan's law is the rule for the negation of quantified proposition.

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17. Multiple quantifiers can be used to quantify propositions with _____ variable?

1. One
2. Two
3. More than one
4. None

Answer: C) More than one

Explanation:

Multiple quantifiers can be used to quantify propositions with more than one variable.

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18. _____ to arrange the multiple universal quantifiers or existential quantifiers in a particular order in order to make the proposition meaningful?

1. It is necessary
2. It is not necessary
3. Sometimes it is necessary
4. None of the above

Answer: B) It is not necessary

Explanation:

It is not necessary to arrange the multiple universal quantifiers or existential quantifiers in a particular order in order to make the proposition meaningful

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19. It is impossible to change the order of the quantifiers of the proposition containing ____ quantifiers without altering the meaning of the proposition?

1. Universal
2. Existential
3. Both A and B
4. None of the above

Answer: C) Both A and B

Explanation:

It is impossible to change the order of the quantifiers of the proposition containing both universal and existential quantifiers without altering the meaning of the proposition.

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20. Proposition ∃x ∀ y p(x,y) means -?

1. There exists some x such that p (x, y) is false for every y.
2. There exists some x such that p (x, y) is true for every x.
3. There exists some y such that p (x, y) is false for every y.
4. There exists some x such that p (x, y) is true for every y.

Answer: D) There exists some x such that p (x, y) is true for every y.

Explanation:

Proposition ∃x ∀ y p(x,y) means there exists some x such that p (x, y) is true for every y.

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