# Logical Inference: First Order Logic Quiz

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Embark on a journey of logical exploration with our "Logical Inference: First Order Logic Quiz." This quiz is designed to test and enhance your understanding of first-order logic, a fundamental concept in formal reasoning and artificial intelligence.

Delve into the intricacies of quantifiers, predicates, and logical relationships that characterize first-order logic. Each question is crafted to challenge your ability to draw valid conclusions from given statements, demonstrating your prowess in logical inference.

Explore the nuances of formalizing arguments, unravel the mysteries of predicate logic, and navigate the landscape of quantifiers with confidence. Whether you're a seasoned logician or a curious learner, this Read morequiz promises an engaging experience that will sharpen your logical reasoning skills.

Prepare to decipher symbolic expressions, apply quantifiers effectively, and showcase your ability to make sound logical inferences. Are you ready to elevate your logical reasoning to the next level? Take the plunge into the First Order Logic Quiz now and unravel the complexities of first-order logic!

## First Order Logic Questions and Answers

• 1.

### Which of the following is a quantifier in first-order logic?

• A.

NOT

• B.

AND

• C.

FOR ALL

• D.

OR

C. FOR ALL
Explanation
In first-order logic, "FOR ALL" (∀) is a universal quantifier that indicates a statement is true for every possible instance of a variable. It is used to express that a particular property or relation holds for all members of a given set.

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• 2.

### In first-order logic, '∃' represents which type of quantifier?

• A.

FOR SOME

• B.

NOT

• C.

IF THEN

• D.

AND

A. FOR SOME
Explanation
In first-order logic, the symbol '∃' represents the existential quantifier, which is equivalent to "FOR SOME." The existential quantifier (∃) is used to express that there exists at least one instance of a variable for which a given statement is true.

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• 3.

### Which of the following is a predicate in first-order logic?

• A.

OR

• B.

AND

• C.

• D.

IS EVEN

D. IS EVEN
Explanation
In first-order logic, a predicate is a statement that contains variables and becomes a proposition when specific values are substituted for these variables. "IS EVEN" is an example of a predicate, as it involves a property (evenness) that can be applied to a variable.

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• 4.

### What does '→' represent in first-order logic?

• A.

XOR

• B.

AND

• C.

NOT

• D.

IMPLIES

D. IMPLIES
Explanation
In first-order logic, the symbol '→' represents the logical connective for implication or conditional. It is read as "implies" or "if-then." The expression P→Q asserts that if proposition P is true, then proposition Q must also be true. If P is false, or if P is true and Q is false, the entire statement is considered true.

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• 5.

### Which logical relationship is represented by the symbol '∨' in first-order logic?

• A.

NOR

• B.

NOT

• C.

XOR

• D.

OR

D. OR
Explanation
In first-order logic, the symbol '∨' represents the logical connective for disjunction or logical OR. The expression P ∨ Q is true if at least one of the propositions  P or Q is true, and it is false only when both P and Q are false.

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• 6.

### What is the negation of '∀x P(x)'?

• A.

∀x NOT P(x)

• B.

∃x ¬P(x)

• C.

∃x NOT P(x)

• D.

∀x P(x)

B. ∃x ¬P(x)
Explanation
The negation of the statement '∀x P(x)' (which reads as "For all x, P(x)") is represented as '∃x ¬P(x)' (which reads as "There exists an x for which P(x) is not true"). In other words, it asserts that it is not the case that every x satisfies the property P; there is at least one x for which P(x) is false.

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• 7.

### Which quantifier is used to express uniqueness in first order logic?

• A.

• B.

∃!

• C.

∀∃

• D.

∃∀

B. ∃!
Explanation
The quantifier used to express uniqueness in first-order logic is: ∃!The symbol ∃! is read as "there exists a unique" and is used to assert that there is exactly one element satisfying a given property. It combines the existential quantifier (∃) with the uniqueness assertion (!). For example, ∃!x P(x) would be read as "There exists a unique x such that P(x) is true."

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• 8.

### What does '↔' stand for in first order logic?

• A.

AND

• B.

IFF

• C.

XOR

• D.

IMPLIES

B. IFF
Explanation
In first-order logic, the symbol '↔' represents the logical connective for biconditional or "if and only if" (IFF). It is read as "if and only if" and is true when both propositions on either side of the symbol have the same truth value (both true or both false) and false otherwise. The expression ( P↔Q ) asserts that  P is true if and only if Q is true, and vice versa.

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• 9.

### Which logical relationship is denoted by '⊕' in first order logic?

• A.

XOR

• B.

AND

• C.

NAND

• D.

NOR

A. XOR
Explanation
In first-order logic, the symbol '⊕' represents the logical connective for XOR (exclusive or). The expression (P ⊕ Q) is true when either P is true or Q is true, but not both. It is false when both P and Q have the same truth value (both true or both false). The symbol '⊕' denotes the exclusive or relationship in logical expressions.

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• 10.

### What is the negation of '∃x P(x)'?

• A.

∃x NOT P(x)

• B.

∀x ¬P(x)

• C.

∀x NOT P(x)

• D.

∃x P(x)

B. ∀x ¬P(x)
Explanation
The correct negation of '∃x P(x)' is: ∀x ¬P(x)

This is read as "For all x, P(x) is not true" or "It is not the case that there exists an x for which P(x) is true." It asserts that for every x, the property P(x) is not true.

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• Current Version
• Nov 29, 2023
Quiz Edited by
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• Nov 28, 2023
Quiz Created by
Surajit Dey

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