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Recent questions in Discrete Mathematics
1
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221
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 $\neg p \rightarrow ((p \rightarrow \neg p) \rightarrow (\neg p \rightarrow p))$
ankitgupta.1729
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in
Mathematical Logic
Apr 15, 2023
by
ankitgupta.1729
411
views
testsbyankitg-dm-2
mathematical-logic
propositional-logic
multiple-selects
1-mark
1
vote
1
answer
222
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)
ankitgupta.1729
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in
Mathematical Logic
Apr 15, 2023
by
ankitgupta.1729
347
views
testsbyankitg-dm-2
mathematical-logic
propositional-logic
multiple-selects
1-mark
0
votes
1
answer
223
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.
ankitgupta.1729
asked
in
Mathematical Logic
Apr 15, 2023
by
ankitgupta.1729
756
views
testsbyankitg-dm-2
mathematical-logic
propositional-logic
multiple-selects
1-mark
5
votes
2
answers
224
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)
ankitgupta.1729
asked
in
Mathematical Logic
Apr 15, 2023
by
ankitgupta.1729
650
views
testsbyankitg-dm-2
mathematical-logic
propositional-logic
2-marks
0
votes
1
answer
225
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.
ankitgupta.1729
asked
in
Mathematical Logic
Apr 15, 2023
by
ankitgupta.1729
280
views
testsbyankitg-dm-2
mathematical-logic
propositional-logic
multiple-selects
2-marks
2
votes
1
answer
226
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 $S$
ankitgupta.1729
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in
Mathematical Logic
Apr 15, 2023
by
ankitgupta.1729
469
views
testsbyankitg-dm-2
mathematical-logic
propositional-logic
multiple-selects
2-marks
3
votes
2
answers
227
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 $P_1,P_2,...,P_n.$
ankitgupta.1729
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in
Mathematical Logic
Apr 15, 2023
by
ankitgupta.1729
618
views
testsbyankitg-dm-2
mathematical-logic
propositional-logic
multiple-selects
2-marks
1
vote
1
answer
228
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 ______
ankitgupta.1729
asked
in
Mathematical Logic
Apr 15, 2023
by
ankitgupta.1729
967
views
testsbyankitg-dm-2
numerical-answers
mathematical-logic
propositional-logic
2-marks
1
vote
2
answers
229
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.
ankitgupta.1729
asked
in
Mathematical Logic
Apr 15, 2023
by
ankitgupta.1729
818
views
testsbyankitg-dm-2
mathematical-logic
propositional-logic
multiple-selects
2-marks
4
votes
3
answers
230
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
ankitgupta.1729
asked
in
Mathematical Logic
Apr 15, 2023
by
ankitgupta.1729
536
views
testsbyankitg-dm-2
mathematical-logic
propositional-logic
2-marks
0
votes
1
answer
231
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
ankitgupta.1729
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in
Mathematical Logic
Apr 15, 2023
by
ankitgupta.1729
1.3k
views
testsbyankitg-dm-2
mathematical-logic
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2-marks
1
vote
1
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232
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
ankitgupta.1729
asked
in
Mathematical Logic
Apr 15, 2023
by
ankitgupta.1729
389
views
testsbyankitg-dm-2
mathematical-logic
propositional-logic
2-marks
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233
Byju's graph theory coloring question
Graph G is obtained by adding vertex s to $K_{3,4}$ and making s adjacent to every vertex of $K_{3,4}$ . The find the minimum number of colours required ot edge-colour is ?
closed
Sahil_Lather
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in
Graph Theory
Apr 15, 2023
by
Sahil_Lather
450
views
graph-coloring
graph-theory
byjus-practice-book
1
vote
1
answer
234
Self Made Question
Consider a connected undirected graph G with n vertices, where n > 4. Suppose that G has the property that every vertex has a degree of at least n/2, i.e., deg(v) ≥ n/2 for all vertices v in G. Prove that G must contain a cycle of length at most 3n/4.
LRU
asked
in
Graph Theory
Apr 14, 2023
by
LRU
328
views
graph-theory
bipartite-graph
self-doubt
0
votes
1
answer
235
Self Made Question
Let G be a bipartite graph with vertex sets V1 and V2, where |V1| = 12 and |V2| = 18. Suppose that G has a perfect matching, which is a set of edges that covers all vertices in G. What is the minimum number of colors needed to properly color G such that no adjacent vertices share the same color, and how does it relate to the chromatic number of G? Justify your answer.
LRU
asked
in
Graph Theory
Apr 14, 2023
by
LRU
262
views
graph-theory
bipartite-graph
numerical-answers
1
vote
1
answer
236
Self Made Question
Consider a bipartite graph G with vertex sets V1 and V2, where |V1| = 10 and |V2| = 15. What is the minimum number of colors needed to properly color G such that no adjacent vertices share the same color? Justify your answer and explain how it is related to the chromatic number of G.
LRU
asked
in
Graph Theory
Apr 14, 2023
by
LRU
204
views
graph-theory
bipartite-graph
numerical-answers
4
votes
1
answer
237
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.
ankitgupta.1729
asked
in
Mathematical Logic
Apr 11, 2023
by
ankitgupta.1729
565
views
testsbyankitg-dm-1
mathematical-logic
propositional-logic
1-mark
5
votes
2
answers
238
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 ______
ankitgupta.1729
asked
in
Mathematical Logic
Apr 11, 2023
by
ankitgupta.1729
548
views
testsbyankitg-dm-1
numerical-answers
mathematical-logic
propositional-logic
1-mark
4
votes
1
answer
239
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
ankitgupta.1729
asked
in
Mathematical Logic
Apr 11, 2023
by
ankitgupta.1729
325
views
testsbyankitg-dm-1
mathematical-logic
propositional-logic
1-mark
0
votes
1
answer
240
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 ______
ankitgupta.1729
asked
in
Mathematical Logic
Apr 11, 2023
by
ankitgupta.1729
266
views
testsbyankitg-dm-1
numerical-answers
mathematical-logic
propositional-logic
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