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Recent questions tagged propositional-logic
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Discrete Mathematics | Propositional Logic | Test 1 | Question: 6
A compound sentence is a $\textit{tautology}$ if it is true independently of the truth values of its component atomic sentences. A sentence is $\textit{atomic}$ if it contains no sentential connectives. Now, consider the following statements: For any ... (iii) are correct (i),(iii) and (iv) are correct (i),(ii) and (iv) are correct
A compound sentence is a $\textit{tautology}$ if it is true independently of the truth values of its component atomic sentences. A sentence is $\textit{atomic}$ if it con...
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Discrete Mathematics | Propositional Logic | Test 1 | Question: 7
The $\textit{well-formed formulas (wff)}$ of propositional logic are obtained by using the following rules: 1. An atomic proposition $\phi$ is a well-formed formula. 2. If $\phi$ ... (P, Q and R are atomic propositions) Total number of well-formed formulas are ______
The $\textit{well-formed formulas (wff)}$ of propositional logic are obtained by using the following rules: 1. An atomic proposition $\phi$ is a well-formed formula. 2. ...
ankitgupta.1729
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Discrete Mathematics | Propositional Logic | Test 1 | Question: 8
Consider the following truth table for the connective $\rightarrow:$ ... (i) and (iii) are correct (i) and (ii) are correct (i), (ii) and (iii) are correct
Consider the following truth table for the connective $\rightarrow:$ $$\begin{array}{c|c|c}p & q & p \rightarrow q \\\hlineT & T & T \\T & F & F \\F & T...
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Discrete Mathematics | Propositional Logic | Test 1 | Question: 9
Consider the following statements: "Ralph is a dog if he's not a puppet" can be formalized as $\neg$ (Ralph is a puppet) $\rightarrow$ (Ralph is a dog) "Ralph is not a dog because he's a puppet" ... correct $(i)$ and $(iii)$ are correct $(i),(ii)$ and $(iii)$ are correct
Consider the following statements: "Ralph is a dog if he’s not a puppet" can be formalized as $\neg$ (Ralph is a puppet) $\rightarrow$ (Ralph is a dog) ...
ankitgupta.1729
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Apr 11, 2023
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Discrete Mathematics | Propositional Logic | Test 1 | Question: 10
Consider the following two statements: i. Sentence $\textit{Neither A nor B}$ can be represented by $A \downarrow B$ where $\downarrow$ is used in Boolean circuits for $\textit{nor}$ function. ii. Sentence $\textit{not at once A and B}$ ... $(i)$ is correct Only $(ii)$ is correct Both $(i)$ and $(ii)$ are correct None of the above
Consider the following two statements: i. Sentence $\textit{Neither A nor B}$ can be represented by $A \downarrow B$ where $\downarrow$ is used in Boolean circui...
ankitgupta.1729
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Apr 11, 2023
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Discrete Mathematics | Propositional Logic | Test 1 | Question: 11
A function $f:\{0,1\}^n \rightarrow \{0,1\}$ is called an $\textit{n-ary Boolean function}$ or $\textit{truth function}.$ We denote their totality by the set $\mathbf{B_n}.$ Now, $f \in \mathbf{B_n}$ is called $\textit{linear}$ ... of $\textit{n-ary linear Boolean functions}$ is: $2^{2^n}$ $2^{2^{n+1}}$ $2^n$ $2^{n+1}$
A function $f:\{0,1\}^n \rightarrow \{0,1\}$ is called an $\textit{n-ary Boolean function}$ or $\textit{truth function}.$ We denote their totality by the set $\m...
ankitgupta.1729
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Apr 11, 2023
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Discrete Mathematics | Propositional Logic | Test 1 | Question: 12
The atomic propositional variables $p_0,p_1,...$ are $\textit{formulas},$ called $\textit{prime formulas},$ also called $\textit{atomic}$ formulas, or simply $\textit{primes}.$ ... a DNF nor a CNF. $p \vee \neg (\neg p \wedge q)$ is either a DNF or a CNF.
The atomic propositional variables $p_0,p_1,...$ are $\textit{formulas},$ called $\textit{prime formulas},$ also called $\textit{atomic}$ formulas, or simply $\textit{pri...
ankitgupta.1729
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Apr 11, 2023
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Discrete Mathematics | Propositional Logic | Test 1 | Question: 13
The set of logical symbols of a propositional language is called the $\textit{logical signature}.$ A logical signature is called $\textit{functionally complete}$ if every Boolean function is representable by a formula in this ... $\{\rightarrow\}$ is $\textit{not}$ functionally complete.
The set of logical symbols of a propositional language is called the $\textit{logical signature}.$ A logical signature is called $\textit{functionally complete}$ if every...
ankitgupta.1729
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Apr 11, 2023
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Discrete Mathematics | Propositional Logic | Test 1 | Question: 14
A compound sentence is a $\textit{tautology}$ if it is true independently of the truth values of its component atomic sentences. A sentence is $\textit{atomic}$ if it contains no sentential connectives. Let $P,Q$ and ... $(P \leftrightarrow P) \leftrightarrow P$ is a tautology Number of correct statements are ______
A compound sentence is a $\textit{tautology}$ if it is true independently of the truth values of its component atomic sentences. A sentence is $\textit{atomic}$ if it con...
ankitgupta.1729
292
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ankitgupta.1729
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Apr 11, 2023
Mathematical Logic
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Discrete Mathematics | Propositional Logic | Test 1 | Question: 15
A compound sentence is a $\textit{tautology}$ if it is true independently of the truth values of its component atomic sentences. A sentence is $\textit{atomic}$ if it contains no sentential connectives. A sentence $P$ ... ) $\neg Q \rightarrow \neg P$ $Q \rightarrow P$ $P \rightarrow Q$ $\neg P \wedge Q$
A compound sentence is a $\textit{tautology}$ if it is true independently of the truth values of its component atomic sentences. A sentence is $\textit{atomic}$ if it con...
ankitgupta.1729
392
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ankitgupta.1729
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Apr 11, 2023
Mathematical Logic
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GO Classes 2024 | Weekly Quiz 7 | Propositional Logic | Question: 1
Let $p,q$ be two atomic propositional assertions. Then which of the following is/are false? $(p \rightarrow q) \vee (p \rightarrow \neg q)$ is a tautology. $(p \rightarrow q) \vee (q \rightarrow p)$ ... $(p \rightarrow q) \vee (\neg q \rightarrow \neg p)$ is a tautology.
Let $p,q$ be two atomic propositional assertions. Then which of the following is/are false?$(p \rightarrow q) \vee (p \rightarrow \neg q)$ is a tautology.$(p \rightarrow ...
GO Classes
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GO Classes
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Apr 5, 2023
Mathematical Logic
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GO Classes 2024 | Weekly Quiz 7 | Propositional Logic | Question: 2
Let’s consider the interpretation $v$ where $v(p) = F, v(q) = T, v(r) = T.$ Which of the following propositional formulas are satisfied by $v$? $(p \rightarrow \neg q) \vee \neg(r \wedge q)$ $(\neg p \vee \neg q) \rightarrow (p \vee \neg r)$ $\neg(\neg p \rightarrow \neg q) \wedge r$ $\neg (\neg p \rightarrow q \wedge \neg r)$
Let’s consider the interpretation $v$ where $v(p) = F, v(q) = T, v(r) = T.$ Which of the following propositional formulas are satisfied by $v$?$(p \rightarrow \neg q) \...
GO Classes
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GO Classes
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Apr 5, 2023
Mathematical Logic
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GO Classes 2024 | Weekly Quiz 7 | Propositional Logic | Question: 3
Consider the following atomic propositions: $\text{R}$: It is Raining $\text{S}$ ... , and vice versa It is raining is equivalent to sonu is sick It is raining or sonu is sick but not both
Consider the following atomic propositions:$\text{R}$: It is Raining$\text{S}$: Sonu is SickWhich of the following is/are correct English Translation of the following log...
GO Classes
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GO Classes
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Apr 5, 2023
Mathematical Logic
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GO Classes 2024 | Weekly Quiz 7 | Propositional Logic | Question: 4
Consider the following arguments. $\text{Argument 1:}$ Kerry errs or Myrna fails to show. If Kerry errs, then he does not break the record. Myrna fails to show. Therefore, Kerry does break the record. $\text{Argument 2:}$ ... ? Only Argument $1$ is valid. Only Argument $2$ is valid. Both Arguments are valid. No Argument is valid.
Consider the following arguments.$\text{Argument 1:}$ Kerry errs or Myrna fails to show. If Kerry errs, then he does not break the record. Myrna fails to show. Therefore,...
GO Classes
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GO Classes
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Apr 5, 2023
Mathematical Logic
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GO Classes 2024 | Weekly Quiz 7 | Propositional Logic | Question: 11
Let $F$ and $G$ be two propositional formula. Which of the following is/are True? $F \vee G$ is a tautology iff at least one of them is a tautology If $F \rightarrow G$ is a tautology and $F$ is a tautology, then $G$ ... $(F \rightarrow G) \wedge (F \rightarrow \neg G)$ is a tautology iff $F$ is a contradiction.
Let $F$ and $G$ be two propositional formula.Which of the following is/are True?$F \vee G$ is a tautology iff at least one of them is a tautologyIf $F \rightarrow G$ is a...
GO Classes
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GO Classes
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Apr 5, 2023
Mathematical Logic
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GO Classes 2024 | Weekly Quiz 7 | Propositional Logic | Question: 12
The implies connective $\rightarrow$ is one of the stranger connectives in propositional logic. Below are a series of statements regarding implications. Which of the following statements is/are TRUE? For any propositions $P$ and $Q,$ ... $R,$ the following statement is always true: $(P \rightarrow Q) \vee (R \rightarrow Q)$.
The “implies” connective “$\rightarrow$” is one of the stranger connectives in propositional logic. Below are a series of statements regarding implications.Which ...
GO Classes
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GO Classes
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Apr 5, 2023
Mathematical Logic
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11
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GO Classes 2024 | Weekly Quiz 7 | Propositional Logic | Question: 13
Consider the following list of $137$ statements: $\left(S_1\right): $ There is exactly $1$ false statement in this list. $\left(S_2\right): $ There are exactly $2$ ... true. It is possible that more than one statement in this list is true. Exactly one statement in this list is true.
Consider the following list of $137$ statements:$\left(S_1\right): $ There is exactly $1$ false statement in this list.$\left(S_2\right): $ There are exactly $2$ false st...
GO Classes
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Apr 5, 2023
Mathematical Logic
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GO Classes 2024 | Weekly Quiz 7 | Propositional Logic | Question: 14
Which of the following logical arguments is/are valid? $\begin{aligned} & P \rightarrow(Q \rightarrow R) \\ & \neg R \\ \therefore & \neg P \\ & \end{aligned}$ ...
Which of the following logical arguments is/are valid?$\begin{aligned} & P \rightarrow(Q \rightarrow R) \\ & \neg R \\ \therefore & \neg P \\ & \end{aligned}$$\begin{alig...
GO Classes
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GO Classes
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Apr 5, 2023
Mathematical Logic
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8
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GO Classes 2024 | Weekly Quiz 7 | Propositional Logic | Question: 15
The Logic Problem, taken from $\text{"WFF'N PROOF, The Game of Logic"}$ has these two assumptions: "Logic is difficult or not many students like logic." "If mathematics is easy, then logic ... is not easy or logic is difficult." "Logic is not difficult or mathematics is not easy."
The Logic Problem, taken from $\text{"WFF'N PROOF, The Game of Logic"}$ has these two assumptions:"Logic is difficult or not many students like logic.""If mathematics is ...
GO Classes
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Apr 5, 2023
Mathematical Logic
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18
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GO Classes 2024 | Weekly Quiz 7 | Propositional Logic | Question: 16
Which of the following statements is/are true? The argument form with premises $p_1, p_2, \ldots, p_n$ and conclusion $q \rightarrow r$ is valid iff the argument form with premises $p_1, p_2, \ldots, p_n, r$, and conclusion $q$ ... the argument form with premises $p_1, p_2, \ldots, p_n, \sim r$, and conclusion $\sim q$ is valid.
Which of the following statements is/are true?The argument form with premises $p_1, p_2, \ldots, p_n$ and conclusion $q \rightarrow r$ is valid iff the argument form with...
GO Classes
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GO Classes
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Mathematical Logic
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