> For the complete documentation index, see [llms.txt](https://nec-license.gitbook.io/books/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://nec-license.gitbook.io/books/9.-artificial-intelligence-and-neural-networks/mcqs/set-5.md).
# set-5
#### 201. \_\_\_\_\_\_ may be either true or false but not other value.
1. Proposition
2. Predicate
3. Quantifier
4. Inference
Show me the answer
**Answer:** 1. Proposition
**Explanation:**
* A **proposition** is a statement that is either true or false, but not both.
* It is a declarative sentence that can be evaluated as true or false.
#### 202. \_\_\_\_\_\_ is the type of the proposition.
1. Simple
2. Compound
3. Both A and B
4. None of above
Show me the answer
**Answer:** 3. Both A and B
**Explanation:**
* Propositions can be **simple** (atomic) or **compound** (composed of multiple propositions connected by logical operators).
* Both types are valid in logic.
#### 203. \_\_\_\_\_\_ are formed from atomic formulas using the logical connectives not, or, if...then, and, if and only if etc.
1. Simple Proposition
2. Compound Proposition
3. Existential Proposition
4. Non-existential Proposition
Show me the answer
**Answer:** 2. Compound Proposition
**Explanation:**
* **Compound propositions** are formed by combining atomic propositions using logical connectives such as AND, OR, NOT, IF...THEN, and IF AND ONLY IF.
* These connectives allow for the creation of more complex logical expressions.
#### 204. Identify the examples of proposition and state which proposition is this.
Eg1: It is raining.\
Eg2: Snow is white.
1. Simple Proposition
2. Compound Proposition
3. Existential Proposition
4. Non-existential Proposition
Show me the answer
**Answer:** 1. Simple Proposition
**Explanation:**
* Both examples are **simple propositions** because they are single, declarative statements that can be evaluated as true or false.
* They do not contain any logical connectives or multiple propositions.
#### 205. Identify the examples of propositions and state which proposition is this.
Eg1. If you study hard you will be rewarded.\
Eg2. The sum of 10 and 20 is not 50.
1. Simple Proposition
2. Compound Proposition
3. Existential Proposition
4. Non-existential Proposition
Show me the answer
**Answer:** 2. Compound Proposition
**Explanation:**
* Both examples are **compound propositions** because they involve logical connectives.
* Eg1 uses "if...then," and Eg2 uses "not," making them compound propositions.
#### 206. Which is used to construct the complex sentences?
1. Connectives
2. Symbols
3. Logical connectives
4. Semantics
Show me the answer
**Answer:** 3. Logical connectives
**Explanation:**
* **Logical connectives** such as AND, OR, NOT, IF...THEN, and IF AND ONLY IF are used to construct complex sentences from simpler propositions.
* These connectives allow for the creation of more sophisticated logical expressions.
#### 207. \_\_\_\_\_\_ is the logical operator.
1. Negation
2. Conjunction
3. Both A and B
4. None of above
Show me the answer
**Answer:** 3. Both A and B
**Explanation:**
* **Negation** (NOT) and **conjunction** (AND) are both logical operators.
* They are used to manipulate and combine propositions in logical expressions.
#### 208. Consider, the proposition P, Identify which logical connectives is this? -P (read "not P")
1. Conjunction
2. Disjunction
3. Negation
4. Exclusive OR
Show me the answer
**Answer:** 3. Negation
**Explanation:**
* The symbol **-P** represents the **negation** of the proposition P.
* Negation is a logical operator that inverts the truth value of a proposition.
#### 209. Consider, P and Q be the propositions, Identify which logical connectives is this? PAQ (read "P and Q")
1. Conjunction
2. Disjunction
3. Negation
4. Exclusive OR
Show me the answer
**Answer:** 1. Conjunction
**Explanation:**
* The expression **PAQ** represents the **conjunction** of P and Q, meaning "P and Q."
* Conjunction is a logical operator that is true only if both P and Q are true.
#### 210. Consider, P and Q be the propositions, Identify which logical connectives is this? PVQ (read "P or Q")
1. Conjunction
2. Disjunction
3. Negation
4. Exclusive OR
Show me the answer
**Answer:** 2. Disjunction
**Explanation:**
* The expression **PVQ** represents the **disjunction** of P and Q, meaning "P or Q."
* Disjunction is a logical operator that is true if at least one of P or Q is true.
#### 211. Consider, P and Q be the propositions, Identify which statement is true for this relation. P→Q (read "P implies Q")
1. Implication of P from Q
2. Implication of Q from P
3. Biconditional from P to Q
4. Biconditional from Q to P
Show me the answer
**Answer:** 2. Implication of Q from P
**Explanation:**
* The expression **P→Q** represents the **implication** of Q from P, meaning "if P is true, then Q is true."
* It is a conditional statement where P is the hypothesis, and Q is the conclusion.
#### 212. Consider, P and Q be the propositions, Identify which logical operator is this? P\@Q
1. Conjunction
2. Disjunction
3. Negation
4. Exclusive OR
Show me the answer
**Answer:** 4. Exclusive OR
**Explanation:**
* The symbol **P\@Q** typically represents the **exclusive OR** (XOR) operation.
* XOR is true if either P or Q is true, but not both.
#### 213. Suppose, P and Q be the propositions. In \_\_\_\_\_\_ statement P→Q, P is called hypothesis (premise or antecedent) and Q is called conclusion or consequence.
1. Simple Statement
2. Conditional Statement
3. Both A and B
4. None of above
Show me the answer
**Answer:** 2. Conditional Statement
**Explanation:**
* The statement **P→Q** is a **conditional statement**, where P is the hypothesis (antecedent), and Q is the conclusion (consequent).
* It represents a logical implication.
#### 214. The conditional statement of P→Q is
1. “if P, then Q”
2. “if P, Q”
3. “P is sufficient for Q”
4. All of above
Show me the answer
**Answer:** 4. All of above
**Explanation:**
* The conditional statement **P→Q** can be expressed in multiple ways, including "if P, then Q," "if P, Q," and "P is sufficient for Q."
* All these forms are valid representations of the implication.
#### 215. To form the \_\_\_\_\_\_ of the conditional statement, interchange the hypothesis and the conclusion. The \_\_\_\_\_\_ of "If it rains, then they cancel hiking" is "If they cancel hiking, then it rains."
1. Converse, Inverse
2. Converse, Converse
3. Inverse, Converse
4. Converse, Contrapositive
Show me the answer
**Answer:** 2. Converse, Converse
**Explanation:**
* The **converse** of a conditional statement is formed by interchanging the hypothesis and the conclusion.
* For example, the converse of "If it rains, then they cancel hiking" is "If they cancel hiking, then it rains."
#### 216. To form the \_\_\_\_\_\_ of the conditional statement, take the negation of both the hypothesis and the conclusion. The \_\_\_\_\_\_ of "If it rains, then they cancel hiking" is "If it does not rain, then they do not cancel hiking."
1. Inverse, Converse
2. Converse, Inverse
3. Inverse, Inverse
4. Converse, Converse
Show me the answer
**Answer:** 3. Inverse, Inverse
**Explanation:**
* The **inverse** of a conditional statement is formed by negating both the hypothesis and the conclusion.
* For example, the inverse of "If it rains, then they cancel hiking" is "If it does not rain, then they do not cancel hiking."
#### 217. To form the \_\_\_\_\_\_ of the conditional statement, interchange the hypothesis and the conclusion of the inverse statement. The \_\_\_\_\_\_ of "If it rains, then they cancel hiking" is "If they do not cancel hiking, then it does not rain."
1. Contrapositive, Contrapositive
2. Converse, Inverse
3. Inverse, Inverse
4. Converse, Converse
Show me the answer
**Answer:** 1. Contrapositive, Contrapositive
**Explanation:**
* The **contrapositive** of a conditional statement is formed by interchanging the hypothesis and the conclusion of the inverse statement.
* For example, the contrapositive of "If it rains, then they cancel hiking" is "If they do not cancel hiking, then it does not rain."
#### 218. Let P and Q be Propositions, In \_\_\_\_\_\_ statement P←→Q, the proposition is "if P and only if Q"
1. Atomic Statement
2. Conditional Statement
3. Bi-conditional Statement
4. None of above
Show me the answer
**Answer:** 3. Bi-conditional Statement
**Explanation:**
* The statement **P←→Q** is a **bi-conditional statement**, meaning "P if and only if Q."
* It is true when both P and Q have the same truth value.
#### 219. The conditional statement of P←→Q is
1. “p is necessary and sufficient for q”
2. “if p then q, and conversely”
3. “p iff q”
4. “p if and only if q”
5. All of above
Show me the answer
**Answer:** 5. All of above
**Explanation:**
* The bi-conditional statement **P←→Q** can be expressed in multiple ways, including "p is necessary and sufficient for q," "if p then q, and conversely," "p iff q," and "p if and only if q."
* All these forms are valid representations of the bi-conditional statement.
#### 220. A proposition that is always true is called a \_\_\_\_\_\_
1. Contradiction
2. Contingency
3. Tautology
4. Hypothesis
Show me the answer
**Answer:** 3. Tautology
**Explanation:**
* A **tautology** is a proposition that is always true, regardless of the truth values of its components.
* It is a statement that is logically valid in all cases.
#### 221. A proposition that is always false is called a \_\_\_\_\_\_
1. Contradiction
2. Contingency
3. Tautology
4. Hypothesis
Show me the answer
**Answer:** 1. Contradiction
**Explanation:**
* A **contradiction** is a proposition that is always false, regardless of the truth values of its components.
* It is a statement that is logically invalid in all cases.
#### 222. A proposition is called a \_\_\_\_\_\_, if that proposition is neither a tautology nor a contradiction.
1. Contradiction
2. Contingency
3. Tautology
4. Hypothesis
Show me the answer
**Answer:** 2. Contingency
**Explanation:**
* A **contingency** is a proposition that is neither a tautology nor a contradiction.
* Its truth value depends on the truth values of its components.
#### 223. Every complete "sentence" contains two parts: a \_\_\_\_\_\_ and a \_\_\_\_\_\_
1. Object, contingency
2. Object, predicate
3. Object, Hypothesis
4. Object, Tautology
Show me the answer
**Answer:** 2. Object, predicate
**Explanation:**
* In logic, a complete sentence consists of an **object** (the subject) and a **predicate** (the property or relation associated with the object).
* For example, in "The sky is blue," "the sky" is the object, and "is blue" is the predicate.
#### 224. Consider an example and identify the predicate.
"The car Ram is driving is red":\
"The sky is red":\
"The cover of this book is red":
1. The predicate is “is red”
2. The predicate is “is driving”
3. The predicate is “the sky”
4. The predicate is “this book”
Show me the answer
**Answer:** 1. The predicate is “is red”
**Explanation:**
* In all three examples, the predicate is "is red," as it describes the property of the object.
* The predicate is the part of the sentence that provides information about the subject.
#### 225. A \_\_\_\_\_\_ is a property that a variable or a finite collection of variables can have.
1. Tautology
2. Predicate
3. Proposition
4. Implication
Show me the answer
**Answer:** 2. Predicate
**Explanation:**
* A **predicate** is a property or relation that can be applied to variables or objects.
* For example, in "x is red," "is red" is the predicate applied to the variable x.
#### 226. P, P^Q, P \rightarrow Q, \neg Q etc. These are the examples of \_\_\_\_\_\_
1. Proof
2. Validity
3. Well-formed-formula
4. Inference
Show me the answer
**Answer:** 3. Well-formed-formula
**Explanation:**
* **Well-formed formulas (WFFs)** are syntactically correct expressions in logic.
* Examples include P, P^Q, P→Q, and ¬Q, which are valid logical expressions.
#### 227. A language element which generates a quantification (such as "every") is called a \_\_\_\_\_\_
1. Proof
2. Quantifier
3. Inference
4. Tautology
Show me the answer
**Answer:** 2. Quantifier
**Explanation:**
* A **quantifier** is a language element that specifies the quantity of a variable in a logical expression.
* Examples include "every," "some," and "all."
#### 228. Two types of quantifiers, which are called the \_\_\_\_\_\_ and the \_\_\_\_\_\_ quantifiers, can quantify the open statements p(x) and q(x,y).
1. Existential
2. Universal
3. Conditional
4. Both A and B
Show me the answer
**Answer:** 4. Both A and B
**Explanation:**
* The two main types of quantifiers are **existential** (e.g., "there exists") and **universal** (e.g., "for all").
* These quantifiers are used to specify the scope of variables in logical expressions.
#### 229. The \_\_\_\_\_\_ quantifier (means "for some x", "for at least one x", or "there exists an x such that"); "for some x, p(x)" is denoted as "∃x, p(x)".
1. Universal
2. Existential
3. Conditional
4. None of above
Show me the answer
**Answer:** 2. Existential
**Explanation:**
* The **existential quantifier** (∃) is used to express that there exists at least one value of x for which p(x) is true.
* It is denoted as "∃x, p(x)."
#### 230. The \_\_\_\_\_\_ quantifier (means "for all x", "for any x", "for each x", or "for every x"): "for all x, all y" is denoted by "∀x ∀y".
1. Universal
2. Existential
3. Conditional
4. None of above
Show me the answer
**Answer:** 1. Universal
**Explanation:**
* The **universal quantifier** (∀) is used to express that a statement is true for all values of x.
* It is denoted as "∀x, p(x)."
#### 231. The \_\_\_\_\_\_ of propositional logic provide the means to perform logical proofs or deductions.
1. Inference rules
2. Commutativity rules
3. Associativity rules
4. Idempotency rules
Show me the answer
**Answer:** 1. Inference rules
**Explanation:**
* **Inference rules** are used in propositional logic to derive conclusions from premises.
* Examples include modus ponens, modus tollens, and hypothetical syllogism.
#### 232. \_\_\_\_\_\_ are the types of inference rules.
1. Modus ponens
2. Modus tollens
3. Both A and B
4. None of above
Show me the answer
**Answer:** 3. Both A and B
**Explanation:**
* **Modus ponens** and **modus tollens** are both types of inference rules used in logical reasoning.
* They are fundamental to deductive reasoning.
#### 233. If P and P \rightarrow Q are both true, we can infer that Q will be true as well in \_\_\_\_\_\_
1. Modus ponens
2. Modus tollens
3. Hypothetical syllogism
4. Disjunctive syllogism
Show me the answer
**Answer:** 1. Modus ponens
**Explanation:**
* **Modus ponens** is an inference rule that states if P is true and P→Q is true, then Q must also be true.
* It is a fundamental rule in logical reasoning.
#### 234. If P \rightarrow Q is true and \neg Q is true, then \neg P will also true in \_\_\_\_\_\_
1. Modus ponens
2. Modus tollens
3. Hypothetical syllogism
4. Disjunctive syllogism
Show me the answer
**Answer:** 2. Modus tollens
**Explanation:**
* **Modus tollens** is an inference rule that states if P→Q is true and ¬Q is true, then ¬P must also be true.
* It is the contrapositive of modus ponens.
#### 235. If P \rightarrow R is true whenever P \rightarrow Q is true, and Q \rightarrow R is true in \_\_\_\_\_\_
1. Modus ponens
2. Modus tollens
3. Hypothetical syllogism
4. Disjunctive syllogism
Show me the answer
**Answer:** 3. Hypothetical syllogism
**Explanation:**
* **Hypothetical syllogism** is an inference rule that states if P→Q and Q→R are true, then P→R must also be true.
* It is used to chain implications together.
#### 236. If PVQ is true, and \neg P is true, then Q will be true in \_\_\_\_\_\_
1. Modus ponens
2. Modus tollens
3. Hypothetical syllogism
4. Disjunctive syllogism
Show me the answer
**Answer:** 4. Disjunctive syllogism
**Explanation:**
* **Disjunctive syllogism** is an inference rule that states if PVQ is true and ¬P is true, then Q must also be true.
* It is used to eliminate one of the disjuncts in a logical disjunction.
#### 237. If P is true, then PVQ will be true in \_\_\_\_\_\_
1. Modus ponens
2. Modus tollens
3. Addition
4. Disjunctive syllogism
Show me the answer
**Answer:** 3. Addition
**Explanation:**
* **Addition** is an inference rule that states if P is true, then PVQ must also be true, regardless of the truth value of Q.
* It is used to introduce a disjunction.
#### 238. If PA Q is true, then Q or P will also be true in \_\_\_\_\_\_
1. Modus ponens
2. Addition
3. Simplification
4. Resolution
Show me the answer
**Answer:** 3. Simplification
**Explanation:**
* **Simplification** is an inference rule that states if PAQ is true, then both P and Q must also be true.
* It is used to break down a conjunction into its individual components.
#### 239. If PVQ and \neg PAR is true, then QVR will also be true in \_\_\_\_\_\_
1. Modus ponens
2. Addition
3. Simplification
4. Resolution
Show me the answer
**Answer:** 4. Resolution
**Explanation:**
* **Resolution** is an inference rule that combines two clauses to produce a new clause.
* In this case, PVQ and ¬PAR resolve to QVR.
#### 240. \_\_\_\_\_\_ is a process of making two different logical atomic expressions identical by finding a substitution.
1. Quantification
2. Unification
3. Resolution
4. Simplification
Show me the answer
**Answer:** 2. Unification
**Explanation:**
* **Unification** is the process of finding a substitution that makes two logical expressions identical.
* It is a key step in many logical inference algorithms, such as resolution.
#### 241. Which is also called single inference rule?
1. Modus Ponens
2. Resolution
3. Modus Tollens
4. Conjunction
Show me the answer
**Answer:** 2. Resolution
**Explanation:**
* **Resolution** is often referred to as a single inference rule because it can be used to derive conclusions from a set of clauses without requiring multiple steps.
* It is a powerful and widely used rule in automated theorem proving.
#### 242. FOPL was developed to extend the expressiveness of \_\_\_\_\_\_.
1. Predicate logic
2. Propositional logic
3. Tautology
4. Quantifiers
Show me the answer
**Answer:** 2. Propositional logic
**Explanation:**
* **First-Order Predicate Logic (FOPL)** was developed to extend the expressiveness of **propositional logic** by introducing quantifiers and predicates.
* This allows for more complex and nuanced logical expressions.
#### 243. Consider the following logic and state if this is valid or not.
Example:\
If All men are mortal = P\
Socrates is a Man = Q\
Socrates is mortal = R\
Then (P & Q) → R
1. Valid
2. Invalid
3. Partially valid
4. Rather not say
Show me the answer
**Answer:** 1. Valid
**Explanation:**
* The argument is **valid** because if all men are mortal (P) and Socrates is a man (Q), then it logically follows that Socrates is mortal (R).
* This is a classic example of a valid syllogism.
#### 244. First Order Predicate Logic (FOPL) is also known as \_\_\_\_\_\_.
1. First Order Predicate Calculus
2. Quantification Theory
3. Lower Order Calculus
4. All of the mentioned above
Show me the answer
**Answer:** 4. All of the mentioned above
**Explanation:**
* **First-Order Predicate Logic (FOPL)** is also known as **First-Order Predicate Calculus**, **Quantification Theory**, and **Lower Order Calculus**.
* These terms are often used interchangeably to refer to the same logical system.
#### 245. In FOPL, constants, variables and functions are known as \_\_\_\_\_\_.
1. Lists
2. Terms
3. Atoms
4. Literals
Show me the answer
**Answer:** 2. Terms
**Explanation:**
* In **First-Order Predicate Logic (FOPL)**, **constants**, **variables**, and **functions** are collectively referred to as **terms**.
* Terms are the basic building blocks of logical expressions in FOPL.
#### 246. In FOPL, predicates are referred to as atomic formulas or \_\_\_\_\_\_.
1. Lists
2. Terms
3. Atoms
4. Literals
Show me the answer
**Answer:** 3. Atoms
**Explanation:**
* In **First-Order Predicate Logic (FOPL)**, **predicates** are referred to as **atomic formulas** or **atoms**.
* These are the simplest forms of logical expressions that cannot be broken down further.
#### 247. In FOPL, when we want to refer to an atom, or its negation we often use the word \_\_\_\_\_\_.
1. Lists
2. Terms
3. Atoms
4. Literals
Show me the answer
**Answer:** 4. Literals
**Explanation:**
* In **First-Order Predicate Logic (FOPL)**, a **literal** is an atom or its negation.
* Literals are used to build more complex logical expressions.
#### 248. Translate English to FOPL: Khusboo likes Pizza.
1. Likes (Khusboo, Pizza)
2. Likes (Pizza, Khusboo)
3. Khusboo (Pizza, likes)
4. Pizza (khusboo, likes)
Show me the answer
**Answer:** 1. Likes (Khusboo, Pizza)
**Explanation:**
* The correct translation of "Khusboo likes Pizza" into FOPL is **Likes(Khusboo, Pizza)**.
* Here, "Likes" is the predicate, "Khusboo" is the subject, and "Pizza" is the object.
#### 249. Translate English to FOPL: Khusboo owns iPhone\_14pro.
1. Owns (Khusboo, iPhone\_14pro)
2. Owns (iPhone\_14pro, Khusboo)
3. Khusboo (iPhone\_14pro, owns)
4. iPhone\_14pro (khusboo, owns)
Show me the answer
**Answer:** 1. Owns (Khusboo, iPhone\_14pro)
**Explanation:**
* The correct translation of "Khusboo owns iPhone\_14pro" into FOPL is **Owns(Khusboo, iPhone\_14pro)**.
* Here, "Owns" is the predicate, "Khusboo" is the subject, and "iPhone\_14pro" is the object.
#### 250. Translate English to FOPL: Charlie is Dog.
1. Charlie (Dog)
2. Dog (Charlie)
3. Charlie → Dog
4. Charlie ←→ Dog
Show me the answer
**Answer:** 2. Dog (Charlie)
**Explanation:**
* The correct translation of "Charlie is Dog" into FOPL is **Dog(Charlie)**.
* Here, "Dog" is the predicate, and "Charlie" is the subject.