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User ankitgupta.1729
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Questions by ankitgupta.1729
3
votes
2
answers
1
Discrete Mathematics | Propositional Logic | Test 2 | Question: 1
Let $\Phi$ be a well-formed formula having atleast one occurrence of atomic variable $x.$ Consider $\Psi$ be any formula. Now, $_x\Phi_{\Psi}$ is the formula obtained by replacing each occurrence of $x$ by $\Psi$ in $\Phi$ and ... Only (i) is correct Only (ii) is correct Both (i) and (ii) are correct None of the above
asked
in
Mathematical Logic
Apr 15, 2023
488
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testsbyankitg-dm-2
mathematical-logic
propositional-logic
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1
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2
Discrete Mathematics | Propositional Logic | Test 2 | Question: 2
Consider the following argument: Either logic is difficult, or not many students like it. If mathematics is easy, then logic is not difficult. $\textit{Therefore,}$ if many students like logic, mathematics is not ... then $P \rightarrow Q$ is a tautology Validity of the given argument can't be determined
asked
in
Mathematical Logic
Apr 15, 2023
388
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testsbyankitg-dm-2
mathematical-logic
propositional-logic
multiple-selects
1-mark
1
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1
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3
Discrete Mathematics | Propositional Logic | Test 2 | Question: 3
Suppose we have to construct a formula that expresses the truth function $\phi$ ... The formula that $\phi$ expresses is $\neg p \rightarrow ((p \rightarrow \neg p) \rightarrow (\neg p \rightarrow p))$
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Mathematical Logic
Apr 15, 2023
412
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testsbyankitg-dm-2
mathematical-logic
propositional-logic
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4
Discrete Mathematics | Propositional Logic | Test 2 | Question: 4
Consider a conditional statement $P \rightarrow Q.$ The proposition $Q \rightarrow P$ is called the $\textit{converse}$ of $P \rightarrow Q.$ The proposition $\neg Q \rightarrow \neg P$ ... If the converse is true, then the inverse is also logically true. (P and Q are distinct atomic sentences)
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in
Mathematical Logic
Apr 15, 2023
349
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mathematical-logic
propositional-logic
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5
Discrete Mathematics | Propositional Logic | Test 2 | Question: 5
A compound proposition is $\textit{satisfiable}$ if there is an assignment of truth values to its variables that makes it true. When no such assignments exists, that is, when the compound proposition is false for all assignments of ... but not valid. Hence, it is a contingency where $P,Q$ and $R$ are distinct atomic propositions.
asked
in
Mathematical Logic
Apr 15, 2023
757
views
testsbyankitg-dm-2
mathematical-logic
propositional-logic
multiple-selects
1-mark
5
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6
Discrete Mathematics | Propositional Logic | Test 2 | Question: 6
How many assignments of truth values to distinct $P_1,P_2,P_3,...,P_n$ with $n \geq 5$ ... $\textbf{Hint}:$ Try to construct the recurrence for the given problem and then solve it)
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in
Mathematical Logic
Apr 15, 2023
657
views
testsbyankitg-dm-2
mathematical-logic
propositional-logic
2-marks
0
votes
1
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7
Discrete Mathematics | Propositional Logic | Test 2 | Question: 7
Suppose two premises are given as: $(1)$ Either Mary gives Peter his toy or Peter is going to cry. $(2)$ Mary does not give Peter his toy. Which one of the following statements is correct ... from the above two premises. Conclusion 'Peter is not going to cry' logically follows from the above two premises.
asked
in
Mathematical Logic
Apr 15, 2023
280
views
testsbyankitg-dm-2
mathematical-logic
propositional-logic
multiple-selects
2-marks
2
votes
1
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8
Discrete Mathematics | Propositional Logic | Test 2 | Question: 8
In the $\textit{theory of inference},$ we begin with a set of formulas which we call $\textit{premises/ hypotheses}$ and using some rules we obtain some other $\textit{given formula}$ ... a logical consequence of given premises Premise $(1)$ and $\neg C$ does not tautologically imply $S$
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in
Mathematical Logic
Apr 15, 2023
470
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testsbyankitg-dm-2
mathematical-logic
propositional-logic
multiple-selects
2-marks
3
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2
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9
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 $P_1,P_2,...,P_n.$
asked
in
Mathematical Logic
Apr 15, 2023
620
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testsbyankitg-dm-2
mathematical-logic
propositional-logic
multiple-selects
2-marks
1
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1
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10
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 ______
asked
in
Mathematical Logic
Apr 15, 2023
968
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testsbyankitg-dm-2
numerical-answers
mathematical-logic
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11
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.
asked
in
Mathematical Logic
Apr 15, 2023
820
views
testsbyankitg-dm-2
mathematical-logic
propositional-logic
multiple-selects
2-marks
4
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3
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12
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
asked
in
Mathematical Logic
Apr 15, 2023
537
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testsbyankitg-dm-2
mathematical-logic
propositional-logic
2-marks
0
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1
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13
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
asked
in
Mathematical Logic
Apr 15, 2023
1.3k
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testsbyankitg-dm-2
mathematical-logic
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2-marks
1
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1
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14
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
asked
in
Mathematical Logic
Apr 15, 2023
392
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testsbyankitg-dm-2
mathematical-logic
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2-marks
4
votes
1
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15
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.
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in
Mathematical Logic
Apr 11, 2023
565
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testsbyankitg-dm-1
mathematical-logic
propositional-logic
1-mark
5
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16
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 ______
asked
in
Mathematical Logic
Apr 11, 2023
552
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testsbyankitg-dm-1
numerical-answers
mathematical-logic
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4
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17
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
asked
in
Mathematical Logic
Apr 11, 2023
326
views
testsbyankitg-dm-1
mathematical-logic
propositional-logic
1-mark
0
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1
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18
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 ______
asked
in
Mathematical Logic
Apr 11, 2023
266
views
testsbyankitg-dm-1
numerical-answers
mathematical-logic
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19
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 $P$ ... ) $\neg P \rightarrow P$ $P \rightarrow \neg P$ $P \vee Q$ $P \vee \neg P$
asked
in
Mathematical Logic
Apr 11, 2023
239
views
testsbyankitg-dm-1
mathematical-logic
propositional-logic
1-mark
multiple-selects
2
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1
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20
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
asked
in
Mathematical Logic
Apr 11, 2023
202
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testsbyankitg-dm-1
mathematical-logic
propositional-logic
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