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Recent questions tagged testsbyankitg-dm-2
3
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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 ...
ankitgupta.1729
502
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ankitgupta.1729
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Apr 15, 2023
Mathematical Logic
testsbyankitg-dm-2
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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
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...
ankitgupta.1729
404
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ankitgupta.1729
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Apr 15, 2023
Mathematical Logic
testsbyankitg-dm-2
mathematical-logic
propositional-logic
multiple-selects
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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 $\neg p \rightarrow ((p \rightarrow \neg p) \rightarrow (\neg p \rightarrow p))$
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...
ankitgupta.1729
431
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ankitgupta.1729
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Apr 15, 2023
Mathematical Logic
testsbyankitg-dm-2
mathematical-logic
propositional-logic
multiple-selects
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1
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1
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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)
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...
ankitgupta.1729
352
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ankitgupta.1729
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Apr 15, 2023
Mathematical Logic
testsbyankitg-dm-2
mathematical-logic
propositional-logic
multiple-selects
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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, ...
ankitgupta.1729
781
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ankitgupta.1729
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Apr 15, 2023
Mathematical Logic
testsbyankitg-dm-2
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5
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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)...
ankitgupta.1729
665
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ankitgupta.1729
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Apr 15, 2023
Mathematical Logic
testsbyankitg-dm-2
mathematical-logic
propositional-logic
2-marks
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0
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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.
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...
ankitgupta.1729
289
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ankitgupta.1729
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Apr 15, 2023
Mathematical Logic
testsbyankitg-dm-2
mathematical-logic
propositional-logic
multiple-selects
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2
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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 $S$
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...
ankitgupta.1729
477
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ankitgupta.1729
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Apr 15, 2023
Mathematical Logic
testsbyankitg-dm-2
mathematical-logic
propositional-logic
multiple-selects
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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 $P_1,P_2,...,P_n.$
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
640
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ankitgupta.1729
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Apr 15, 2023
Mathematical Logic
testsbyankitg-dm-2
mathematical-logic
propositional-logic
multiple-selects
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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 ______
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
998
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ankitgupta.1729
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Apr 15, 2023
Mathematical Logic
testsbyankitg-dm-2
numerical-answers
mathematical-logic
propositional-logic
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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 ...
ankitgupta.1729
887
views
ankitgupta.1729
asked
Apr 15, 2023
Mathematical Logic
testsbyankitg-dm-2
mathematical-logic
propositional-logic
multiple-selects
2-marks
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4
votes
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
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
545
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ankitgupta.1729
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Apr 15, 2023
Mathematical Logic
testsbyankitg-dm-2
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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
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
1.4k
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ankitgupta.1729
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Apr 15, 2023
Mathematical Logic
testsbyankitg-dm-2
mathematical-logic
propositional-logic
2-marks
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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
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
394
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ankitgupta.1729
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Apr 15, 2023
Mathematical Logic
testsbyankitg-dm-2
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