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Recent activity by ankitgupta.1729

2 answers
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 $\text{TRUE}?$ $f \in O(g)$ $f \in \Omega(g)$ $f \in o(g)$ $f \in \Theta(g)$
answered in Algorithms May 24
2.0k views
  • 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
answered in 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 $\lambda_{1}+\lambda_{2}+\lambda_{3}+\lambda_{4}+\lambda_{5}=$____________
answer edited in Linear Algebra May 18
2.2k views
  • gatecse-2023
  • linear-algebra
  • eigen-value
  • numerical-answers
  • 1-mark
3 answers
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 ... $\exists y \forall x(P(x) \Longrightarrow Q(x, y))$ $\exists x(P(x) \wedge \exists y Q(x, y))$
answer edited in Mathematical Logic May 18
2.2k views
  • gatecse-2023
  • mathematical-logic
  • first-order-logic
  • multiple-selects
  • 1-mark
1 answer
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?????
commented in 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) $O(n)$ $\Omega(n \log n)$ $O( \log n)$ $O(n^2)$
comment moved 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 in 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 ______
commented in 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 views
  • testsbyankitg-dm-2
  • mathematical-logic
  • propositional-logic
  • multiple-selects
  • 2-marks
1 answer
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)
answer selected in Mathematical Logic Apr 20
115 views
  • testsbyankitg-dm-2
  • mathematical-logic
  • propositional-logic
  • multiple-selects
  • 1-mark
2 answers
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 answer
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 answer
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 ______
commented in 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
commented in Mathematical Logic Apr 19
117 views
  • testsbyankitg-dm-2
  • mathematical-logic
  • propositional-logic
  • 2-marks
2 answers
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
asked in Mathematical Logic Apr 16
127 views
  • 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
asked in Mathematical Logic Apr 16
67 views
  • testsbyankitg-dm-2
  • mathematical-logic
  • propositional-logic
  • multiple-selects
  • 1-mark
1 answer
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 $\neg p \rightarrow ((p \rightarrow \neg p) \rightarrow (\neg p \rightarrow p))$
asked in Mathematical Logic Apr 16
104 views
  • testsbyankitg-dm-2
  • mathematical-logic
  • propositional-logic
  • multiple-selects
  • 1-mark
1 answer
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.
asked in 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 answers
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 $P_1,P_2,...,P_n.$
asked 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
asked in 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
commented in 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 $P$ ... ) $\neg Q \rightarrow \neg P$ $Q \rightarrow P$ $P \rightarrow Q$ $\neg P \wedge Q$
commented in 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 in 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.
asked in 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 ______
asked in Mathematical Logic Apr 11
188 views
  • testsbyankitg-dm-1
  • numerical-answers
  • mathematical-logic
  • propositional-logic
  • 1-mark
1 answer
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
asked in Mathematical Logic Apr 11
104 views
  • testsbyankitg-dm-1
  • mathematical-logic
  • propositional-logic
  • 1-mark
1 answer
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 ______
asked in Mathematical Logic Apr 11
127 views
  • testsbyankitg-dm-1
  • numerical-answers
  • mathematical-logic
  • propositional-logic
  • 1-mark
1 answer
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 $P$ ... ) $\neg P \rightarrow P$ $P \rightarrow \neg P$ $P \vee Q$ $P \vee \neg P$
asked in Mathematical Logic Apr 11
78 views
  • testsbyankitg-dm-1
  • mathematical-logic
  • propositional-logic
  • 1-mark
  • multiple-selects

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