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.