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Questions by ankitgupta.1729
3
votes
2
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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
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 ...
503
views
asked
Apr 15, 2023
Mathematical Logic
testsbyankitg-dm-2
mathematical-logic
propositional-logic
1-mark
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1
votes
1
answer
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
Consider the following argument: Either logic is difficult, or not many students like it. If mathematics is easy, then logic is not difficult. $\textit{Therefor...
404
views
asked
Apr 15, 2023
Mathematical Logic
testsbyankitg-dm-2
mathematical-logic
propositional-logic
multiple-selects
1-mark
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1
votes
1
answer
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 $\neg p \rightarrow ((p \rightarrow \neg p) \rightarrow (\neg p \rightarrow p))$
Suppose we have to construct a formula that expresses the truth function $\phi$ given by: $$\begin{array}{c|c|c}p & q & \phi \\\hlineT & T & T \\T & F & T \\F...
431
views
asked
Apr 15, 2023
Mathematical Logic
testsbyankitg-dm-2
mathematical-logic
propositional-logic
multiple-selects
1-mark
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1
votes
1
answer
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)
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 \rig...
352
views
asked
Apr 15, 2023
Mathematical Logic
testsbyankitg-dm-2
mathematical-logic
propositional-logic
multiple-selects
1-mark
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0
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1
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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.
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, ...
782
views
asked
Apr 15, 2023
Mathematical Logic
testsbyankitg-dm-2
mathematical-logic
propositional-logic
multiple-selects
1-mark
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5
votes
2
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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)
How many assignments of truth values to distinct $P_1,P_2,P_3,...,P_n$ with $n \geq 5$ are there for which $(...(((P_1 \rightarrow P_2) \rightarrow P_3 ) \rightarrow P_4)...
671
views
asked
Apr 15, 2023
Mathematical Logic
testsbyankitg-dm-2
mathematical-logic
propositional-logic
2-marks
+
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0
votes
1
answer
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.
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 th...
291
views
asked
Apr 15, 2023
Mathematical Logic
testsbyankitg-dm-2
mathematical-logic
propositional-logic
multiple-selects
2-marks
+
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2
votes
1
answer
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 $S$
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{gi...
477
views
asked
Apr 15, 2023
Mathematical Logic
testsbyankitg-dm-2
mathematical-logic
propositional-logic
multiple-selects
2-marks
+
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3
votes
2
answers
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 $P_1,P_2,...,P_n.$
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...
643
views
asked
Apr 15, 2023
Mathematical Logic
testsbyankitg-dm-2
mathematical-logic
propositional-logic
multiple-selects
2-marks
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1
votes
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 ______
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. �...
1.0k
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Apr 15, 2023
Mathematical Logic
testsbyankitg-dm-2
numerical-answers
mathematical-logic
propositional-logic
2-marks
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1
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2
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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.
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 ...
887
views
asked
Apr 15, 2023
Mathematical Logic
testsbyankitg-dm-2
mathematical-logic
propositional-logic
multiple-selects
2-marks
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4
votes
3
answers
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
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 ...
545
views
asked
Apr 15, 2023
Mathematical Logic
testsbyankitg-dm-2
mathematical-logic
propositional-logic
2-marks
+
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0
votes
1
answer
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
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....
1.4k
views
asked
Apr 15, 2023
Mathematical Logic
testsbyankitg-dm-2
mathematical-logic
propositional-logic
2-marks
+
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1
votes
1
answer
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
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 $\vee$. ...
395
views
asked
Apr 15, 2023
Mathematical Logic
testsbyankitg-dm-2
mathematical-logic
propositional-logic
2-marks
+
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4
votes
1
answer
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.
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...
562
views
asked
Apr 11, 2023
Mathematical Logic
testsbyankitg-dm-1
mathematical-logic
propositional-logic
1-mark
+
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5
votes
2
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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 ______
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...
561
views
asked
Apr 11, 2023
Mathematical Logic
testsbyankitg-dm-1
numerical-answers
mathematical-logic
propositional-logic
1-mark
+
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4
votes
1
answer
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
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 ...
339
views
asked
Apr 11, 2023
Mathematical Logic
testsbyankitg-dm-1
mathematical-logic
propositional-logic
1-mark
+
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0
votes
1
answer
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 ______
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...
286
views
asked
Apr 11, 2023
Mathematical Logic
testsbyankitg-dm-1
numerical-answers
mathematical-logic
propositional-logic
1-mark
+
–
1
votes
1
answer
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 $P$ ... ) $\neg P \rightarrow P$ $P \rightarrow \neg P$ $P \vee Q$ $P \vee \neg P$
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...
250
views
asked
Apr 11, 2023
Mathematical Logic
testsbyankitg-dm-1
mathematical-logic
propositional-logic
1-mark
multiple-selects
+
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2
votes
1
answer
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
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...
211
views
asked
Apr 11, 2023
Mathematical Logic
testsbyankitg-dm-1
mathematical-logic
propositional-logic
1-mark
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