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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
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121
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
397
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ankitgupta.1729
asked
Apr 15, 2023
Mathematical Logic
testsbyankitg-dm-2
mathematical-logic
propositional-logic
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122
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
570
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ankitgupta.1729
asked
Apr 11, 2023
Mathematical Logic
testsbyankitg-dm-1
mathematical-logic
propositional-logic
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123
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
568
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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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4
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124
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
342
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ankitgupta.1729
asked
Apr 11, 2023
Mathematical Logic
testsbyankitg-dm-1
mathematical-logic
propositional-logic
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125
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
295
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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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126
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
254
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ankitgupta.1729
asked
Apr 11, 2023
Mathematical Logic
testsbyankitg-dm-1
mathematical-logic
propositional-logic
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multiple-selects
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2
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127
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
213
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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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128
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
637
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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: 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
254
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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: 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
391
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ankitgupta.1729
asked
Apr 11, 2023
Mathematical Logic
testsbyankitg-dm-1
mathematical-logic
propositional-logic
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3
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131
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
196
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ankitgupta.1729
asked
Apr 11, 2023
Mathematical Logic
testsbyankitg-dm-1
mathematical-logic
propositional-logic
2-marks
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5
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132
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
464
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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: 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
531
views
ankitgupta.1729
asked
Apr 11, 2023
Mathematical Logic
testsbyankitg-dm-1
mathematical-logic
propositional-logic
multiple-selects
2-marks
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2
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1
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134
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
293
views
ankitgupta.1729
asked
Apr 11, 2023
Mathematical Logic
testsbyankitg-dm-1
mathematical-logic
propositional-logic
multiple-selects
2-marks
+
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4
votes
1
answer
135
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
318
views
ankitgupta.1729
asked
Apr 11, 2023
Mathematical Logic
testsbyankitg-dm-1
numerical-answers
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