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User ankitgupta.1729
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Recent activity by ankitgupta.1729
2
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1
GATE CSE 2023 | Question: 19
Let $f$ and $g$ be functions of natural numbers given by $f(n)=n$ and $g(n)=n^{2}.$ Which of the following statements is/are $\text{TRUE}?$ $f \in O(g)$ $f \in \Omega(g)$ $f \in o(g)$ $f \in \Theta(g)$
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Algorithms
May 24
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gatecse-2023
algorithms
asymptotic-notations
multiple-selects
1-mark
1
answer
2
Find the value of [v]e wherev is a vector space and e is a list of polynomials
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Mathematical Logic
May 18
57
views
linear-algebra
2
answers
3
GATE CSE 2023 | Question: 20
Let $A$ be the adjacency matrix of the graph with vertices $\{1,2,3,4,5\}.$ Let $\lambda_{1}, \lambda_{2}, \lambda_{3}, \lambda_{4}$, and $\lambda_{5}$ be the five eigenvalues of $A$. Note that these eigenvalues need not be distinct. The value of $\lambda_{1}+\lambda_{2}+\lambda_{3}+\lambda_{4}+\lambda_{5}=$____________
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Linear Algebra
May 18
2.2k
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gatecse-2023
linear-algebra
eigen-value
numerical-answers
1-mark
3
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4
GATE CSE 2023 | Question: 16
Geetha has a conjecture about integers, which is of the form \[ \forall x(P(x) \Longrightarrow \exists y Q(x, y)), \] where $P$ is a statement about integers, and $Q$ is a statement about pairs of integers. Which of the following (one or more) option(s) would imply ... $\exists y \forall x(P(x) \Longrightarrow Q(x, y))$ $\exists x(P(x) \wedge \exists y Q(x, y))$
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Mathematical Logic
May 18
2.2k
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gatecse-2023
mathematical-logic
first-order-logic
multiple-selects
1-mark
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5
Proposition Logic doubt
Given: (p$ \vee$ q) is True. Find the truth value of statements, 1. p is false or q is true. (Can't determine) 2. If p is false then q is true. (True) is my answer correct?????
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Mathematical Logic
May 14
170
views
discrete-mathematics
propositional-logic
mathematical-logic
1
answer
6
GO Classes 2023 | IIITH Mock Test 3 | Question: 11
Maximum Subarray Sum problem is to find the subarray with maximum sum. For example, given an array $\{12, -13, -5, 25, -20, 30, 10\}$, the maximum subarray sum is $45$. The best possible algorithm to compute the maximum subarray sum will run in (Mark all the appropriate choices) $O(n)$ $\Omega(n \log n)$ $O( \log n)$ $O(n^2)$
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in
Algorithms
May 14
234
views
goclasses2023-iiith-mock-3
goclasses
algorithms
time-complexity
algorithm-design
multiple-selects
1-mark
3
answers
7
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
answer selected
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Mathematical Logic
Apr 28
206
views
testsbyankitg-dm-2
mathematical-logic
propositional-logic
2-marks
0
answers
8
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 ______
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Mathematical Logic
Apr 20
222
views
testsbyankitg-dm-1
numerical-answers
mathematical-logic
propositional-logic
2-marks
1
answer
9
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 $S$
answer edited
in
Mathematical Logic
Apr 20
100
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testsbyankitg-dm-2
mathematical-logic
propositional-logic
multiple-selects
2-marks
1
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10
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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Mathematical Logic
Apr 20
115
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testsbyankitg-dm-2
mathematical-logic
propositional-logic
multiple-selects
1-mark
2
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11
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)
answer selected
in
Mathematical Logic
Apr 20
242
views
testsbyankitg-dm-2
mathematical-logic
propositional-logic
2-marks
1
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12
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 ______
answer selected
in
Mathematical Logic
Apr 20
102
views
testsbyankitg-dm-2
numerical-answers
mathematical-logic
propositional-logic
2-marks
1
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13
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 ______
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Mathematical Logic
Apr 19
136
views
testsbyankitg-dm-1
numerical-answers
mathematical-logic
propositional-logic
2-marks
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
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Mathematical Logic
Apr 19
117
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testsbyankitg-dm-2
mathematical-logic
propositional-logic
2-marks
2
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15
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
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Mathematical Logic
Apr 16
127
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testsbyankitg-dm-2
mathematical-logic
propositional-logic
1-mark
1
answer
16
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 ... argument then $P \rightarrow Q$ is a tautology Validity of the given argument can't be determined
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Mathematical Logic
Apr 16
67
views
testsbyankitg-dm-2
mathematical-logic
propositional-logic
multiple-selects
1-mark
1
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17
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 16
104
views
testsbyankitg-dm-2
mathematical-logic
propositional-logic
multiple-selects
1-mark
1
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18
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.
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Mathematical Logic
Apr 16
63
views
testsbyankitg-dm-2
mathematical-logic
propositional-logic
multiple-selects
1-mark
1
answer
19
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 ? ... follows from the above two premises. Conclusion 'Peter is not going to cry' logically follows from the above two premises.
asked
in
Mathematical Logic
Apr 16
57
views
testsbyankitg-dm-2
mathematical-logic
propositional-logic
multiple-selects
2-marks
2
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20
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 the ... $R,$ then we $\textit{can't}$ infer $R \rightarrow S$ from $P_1,P_2,...,P_n.$
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in
Mathematical Logic
Apr 16
156
views
testsbyankitg-dm-2
mathematical-logic
propositional-logic
multiple-selects
2-marks
2
answers
21
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 will ... $P \rightarrow Q$ is a tautology. Validity of the given argument can't be determined.
asked
in
Mathematical Logic
Apr 16
120
views
testsbyankitg-dm-2
mathematical-logic
propositional-logic
multiple-selects
2-marks
1
answer
22
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
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Mathematical Logic
Apr 16
103
views
testsbyankitg-dm-2
mathematical-logic
propositional-logic
2-marks
0
answers
23
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
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Mathematical Logic
Apr 13
116
views
testsbyankitg-dm-1
mathematical-logic
propositional-logic
2-marks
1
answer
24
Discrete Mathematics | Propositional Logic | Test 1 | Question: 15
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 $P$ ... ) $\neg Q \rightarrow \neg P$ $Q \rightarrow P$ $P \rightarrow Q$ $\neg P \wedge Q$
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Mathematical Logic
Apr 12
102
views
testsbyankitg-dm-1
mathematical-logic
propositional-logic
multiple-selects
2-marks
0
answers
25
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.
commented
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Mathematical Logic
Apr 12
121
views
testsbyankitg-dm-1
mathematical-logic
propositional-logic
multiple-selects
2-marks
1
answer
26
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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Mathematical Logic
Apr 11
189
views
testsbyankitg-dm-1
mathematical-logic
propositional-logic
1-mark
2
answers
27
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 ______
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in
Mathematical Logic
Apr 11
188
views
testsbyankitg-dm-1
numerical-answers
mathematical-logic
propositional-logic
1-mark
1
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28
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
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in
Mathematical Logic
Apr 11
104
views
testsbyankitg-dm-1
mathematical-logic
propositional-logic
1-mark
1
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29
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 ______
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in
Mathematical Logic
Apr 11
127
views
testsbyankitg-dm-1
numerical-answers
mathematical-logic
propositional-logic
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1
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30
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 $P$ ... ) $\neg P \rightarrow P$ $P \rightarrow \neg P$ $P \vee Q$ $P \vee \neg P$
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Mathematical Logic
Apr 11
78
views
testsbyankitg-dm-1
mathematical-logic
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