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Webpage for Mathematical Logic
Important Question Types:
Checking validity of First Order Logic Statements
Checking validity of Propositional Logic
Recent questions tagged mathematical-logic
3
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2
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121
Discrete Mathematics | Propositional Logic | Test 2 | Question: 9
To decide an argument is $\textit{valid}$ with $n$ distinct premises as $P_1,P_2,...,P_n$ and conclusion $C$, we need to decide whether $(P_1 \wedge P_2 \wedge...\wedge P_n) \rightarrow C$ is tautology or not. Which of ... $R,$ then we $\textit{can't}$ infer $R \rightarrow S$ from $P_1,P_2,...,P_n.$
To decide an argument is $\textit{valid}$ with $n$ distinct premises as $P_1,P_2,...,P_n$ and conclusion $C$, we need to decide whether $(P_1 \wedge P_2 \wedge...\wedge...
ankitgupta.1729
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ankitgupta.1729
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Apr 15, 2023
Mathematical Logic
testsbyankitg-dm-2
mathematical-logic
propositional-logic
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122
Discrete Mathematics | Propositional Logic | Test 2 | Question: 10
Premises $P_1,P_2,...,P_n$ infer/derive a conclusion $Q$ if and only if the conditional $(P_1 \wedge P_2 \wedge...\wedge P_n) \rightarrow Q$ is a tautology. Consider the following statements: From $P$ ... $P$, $Q$ and $R$ are distinct atomic sentences ) Number of correct statements are ______
Premises $P_1,P_2,...,P_n$ infer/derive a conclusion $Q$ if and only if the conditional $(P_1 \wedge P_2 \wedge...\wedge P_n) \rightarrow Q$ is a tautology. �...
ankitgupta.1729
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ankitgupta.1729
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Apr 15, 2023
Mathematical Logic
testsbyankitg-dm-2
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123
Discrete Mathematics | Propositional Logic | Test 2 | Question: 11
Consider the following argument: If either wages or prices are raised, there will be inflation. If there is inflation, then either Congress must regulate it or the people will suffer. If the people suffer, Congressmen ... $P \rightarrow Q$ is a tautology. Validity of the given argument can't be determined.
Consider the following argument: If either wages or prices are raised, there will be inflation. If there is inflation, then either Congress must regulate it or ...
ankitgupta.1729
1.0k
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ankitgupta.1729
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Apr 15, 2023
Mathematical Logic
testsbyankitg-dm-2
mathematical-logic
propositional-logic
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124
Discrete Mathematics | Propositional Logic | Test 2 | Question: 12
Two sentences are said to be $\textit{contradictory}$ if one is negation of the other. A $\textit{contradiction}$ is a conjunction of two contradictory sentences i.e. it is a conjunction of the form $S \wedge \neg S.$ A set ... Only $(ii)$ is correct Both $(i)$ and $(ii)$ are correct None of the above
Two sentences are said to be $\textit{contradictory}$ if one is negation of the other. A $\textit{contradiction}$ is a conjunction of two contradictory sentences i.e. it ...
ankitgupta.1729
577
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ankitgupta.1729
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Apr 15, 2023
Mathematical Logic
testsbyankitg-dm-2
mathematical-logic
propositional-logic
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125
Discrete Mathematics | Propositional Logic | Test 2 | Question: 13
The consistency of a set of premises whose logical structure may be expressed by sentential connectives alone may be determined directly by a mechanical truth table test. The truth table for the conjunction of the premises is constructed. ... Both systems $(i)$ and $(ii)$ are consistent None of the systems are consistent
The consistency of a set of premises whose logical structure may be expressed by sentential connectives alone may be determined directly by a mechanical truth table test....
ankitgupta.1729
1.5k
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ankitgupta.1729
asked
Apr 15, 2023
Mathematical Logic
testsbyankitg-dm-2
mathematical-logic
propositional-logic
2-marks
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1
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126
Discrete Mathematics | Propositional Logic | Test 2 | Question: 14
The $\textit{dual}$ $P^d$ of a formula $P$ involving the connectives $\{\wedge,\vee, \neg \}$ is obtained by interchanging $\vee$ with $\wedge$ and $\wedge$ with $\vee$ ... correct Only $(ii)$ is correct Both $(i)$ and $(ii)$ are correct None of the above
The $\textit{dual}$ $P^d$ of a formula $P$ involving the connectives $\{\wedge,\vee, \neg \}$ is obtained by interchanging $\vee$ with $\wedge$ and $\wedge$ with $\vee$. ...
ankitgupta.1729
401
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ankitgupta.1729
asked
Apr 15, 2023
Mathematical Logic
testsbyankitg-dm-2
mathematical-logic
propositional-logic
2-marks
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127
Discrete Mathematics | Propositional Logic | Test 1 | Question: 1
A Proposition is a written or uttered declarative sentence used in such a way that it is true or false, but not both. Now, Consider the following statement: $S:$ If George is a duck then Ralph is a dog and Dusty is a horse'. ... and there is only one way to parse it. $S$ is ambiguous and there are three ways to parse it.
A Proposition is a written or uttered declarative sentence used in such a way that it is true or false, but not both. Now, Consider the following statement:$S:$ ‘If Geo...
ankitgupta.1729
582
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ankitgupta.1729
asked
Apr 11, 2023
Mathematical Logic
testsbyankitg-dm-1
mathematical-logic
propositional-logic
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128
Discrete Mathematics | Propositional Logic | Test 1 | Question: 2
Consider the following statements: $A \wedge B$ can be a Formalization of English connective $\textit{A but B}$ $B \rightarrow A$ is a Formalization of English connective $\textit{A only if B}$ $A \rightarrow B$ is ... $\textit{A or else B}$ Number of correct statements are ______
Consider the following statements: $A \wedge B$ can be a Formalization of English connective $\textit{A but B}$ $B \rightarrow A$ is a Formalization of English...
ankitgupta.1729
581
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ankitgupta.1729
asked
Apr 11, 2023
Mathematical Logic
testsbyankitg-dm-1
numerical-answers
mathematical-logic
propositional-logic
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129
Discrete Mathematics | Propositional Logic | Test 1 | Question: 3
Statements $P$ and $Q$ are said to be logically equivalent if they have the same truth value in every model. Now, Consider the following statements: i. Sentences $\textit{A provided B}$ and $\textit{(not A) or B}$ ... $(i)$ is correct Only $(ii)$ is correct Both $(i)$ and $(ii)$ are correct None of the above
Statements $P$ and $Q$ are said to be logically equivalent if they have the same truth value in every model. Now, Consider the following statements: i. Sentences ...
ankitgupta.1729
357
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ankitgupta.1729
asked
Apr 11, 2023
Mathematical Logic
testsbyankitg-dm-1
mathematical-logic
propositional-logic
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130
Discrete Mathematics | Propositional Logic | Test 1 | Question: 4
A function $f:\{0,1\}^n \rightarrow \{0,1\}$ is called an $\textit{n-ary Boolean function}$ or $\textit{truth function}$. The number of unary Boolean functions is ______
A function $f:\{0,1\}^n \rightarrow \{0,1\}$ is called an $\textit{n-ary Boolean function}$ or $\textit{truth function}$. The number of unary Boolean functions...
ankitgupta.1729
297
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ankitgupta.1729
asked
Apr 11, 2023
Mathematical Logic
testsbyankitg-dm-1
numerical-answers
mathematical-logic
propositional-logic
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131
Discrete Mathematics | Propositional Logic | Test 1 | Question: 5
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 $P$ ... ) $\neg P \rightarrow P$ $P \rightarrow \neg P$ $P \vee Q$ $P \vee \neg P$
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
268
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ankitgupta.1729
asked
Apr 11, 2023
Mathematical Logic
testsbyankitg-dm-1
mathematical-logic
propositional-logic
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2
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132
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...
ankitgupta.1729
218
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ankitgupta.1729
asked
Apr 11, 2023
Mathematical Logic
testsbyankitg-dm-1
mathematical-logic
propositional-logic
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6
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133
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
656
views
ankitgupta.1729
asked
Apr 11, 2023
Mathematical Logic
testsbyankitg-dm-1
numerical-answers
mathematical-logic
propositional-logic
2-marks
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3
votes
1
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134
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...
ankitgupta.1729
259
views
ankitgupta.1729
asked
Apr 11, 2023
Mathematical Logic
testsbyankitg-dm-1
mathematical-logic
propositional-logic
2-marks
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2
votes
0
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135
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
399
views
ankitgupta.1729
asked
Apr 11, 2023
Mathematical Logic
testsbyankitg-dm-1
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