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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?**

- Statics
- Variables
- Numbers
- None

**Answer:** B) Variables

**Explanation:**

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

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

- Domain
- Co-domain
- Both a and b
- None of the above

**Answer:** A) Domain

**Explanation:**

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

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

- Authorizing a value to a variable
- Quantifying variable
- Both A and B
- 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.

**4. A ____ quantifies a variable of a predicate?**

- Proposition
- Quantity
- Quality
- Quantifier

**Answer:** D) Quantifier

**Explanation:**

A quantifier quantifies a variable of a predicate.

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

- 2
- 3
- 4
- 5

**Answer:** A) 2

**Explanation:**

There are 2 types of quantifier in predicate logic.

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

- Existential
- Universal
- Both A and B
- None of the above

**Answer:** C) Both A and B

**Explanation:**

The types of quantifier in predicate logic are -

- Existential
- Universal

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

- x∃p(x)
- p(x)∃x
- p(x)x∃
- ∃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).

**8. ∃x p(x) is read as -?**

- There exists one value in the universe of variable x such that p(x) is true
- There exists at least one value in the universe of variable x such that p(x) is false
- There exists at least one value in the universe of variable p(x) such that x is true
- 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”.

**9. Quantifier ∃ is called _____ quantifier?**

- Existential
- Universal
- Both A and B
- None of the above

**Answer:** A) Existential

**Explanation:**

Quantifier ∃ is called existential quantifier.

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

- (∃x∈A)p(x)
- ∃x∈A such that p (x)
- (∃x)p(x)
- All of the above

**Answer:** D) All of the above

**Explanation:**

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

- (∃x∈A)p(x)
- ∃x∈A such that p (x)
- (∃x)p(x)

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

- x∀p(x)
- p(x),∃∀
- p(x),x∀
- ∀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).

**12. ∀x,p(x) is read as -?**

- For every x∈U,p(x) isfalse
- For every x∈p(x) is true
- For every x∈U,p(x) is true
- 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.

**13. Quantifier ∀ is called ____ quantifier?**

- Existential
- Universal
- Both A and B
- None of the above

**Answer:** B) Universal

**Explanation:**

Quantifier ∀ is called universal quantifier.

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

- ∀x∈A,p(x)
- p(x), ∀x ∈A
- ∀x,p(x)
- All of the above

**Answer:** D) All of the above

**Explanation:**

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

- ∀x∈A,p(x)
- p(x), ∀x ∈A
- ∀x,p(x)

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

- An existentially quantified proposition arises from negating a universally quantified proposition
- An universally quantified proposition arises from negating a existentially quantified proposition
- Both A and B
- None of the above

**Answer:** C) Both A and B

**Explanation:**

The following statement is TRUE -

- An existentially quantified proposition arises from negating a universally quantified proposition
- An universally quantified proposition arises from negating a existentially quantified proposition

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

- Dissociative law
- Associative law
- Demorgan’s law
- Identity law

**Answer:** C) Demorgan's law

**Explanation:**

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

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

- One
- Two
- More than one
- None

**Answer:** C) More than one

**Explanation:**

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

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

- It is necessary
- It is not necessary
- Sometimes it is necessary
- 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

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

- Universal
- Existential
- Both A and B
- 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.

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

- There exists some x such that p (x, y) is false for every y.
- There exists some x such that p (x, y) is true for every x.
- There exists some y such that p (x, y) is false for every y.
- 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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