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Recent questions in Discrete Mathematics
3
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301
Discrete Mathematics | Propositional Logic | Test 1 | Question: 8
Consider the following truth table for the connective $\rightarrow:$ ... (i) and (iii) are correct (i) and (ii) are correct (i), (ii) and (iii) are correct
Consider the following truth table for the connective $\rightarrow:$ $$\begin{array}{c|c|c}p & q & p \rightarrow q \\\hlineT & T & T \\T & F & F \\F & T...
ankitgupta.1729
257
views
ankitgupta.1729
asked
Apr 11, 2023
Mathematical Logic
testsbyankitg-dm-1
mathematical-logic
propositional-logic
2-marks
+
–
2
votes
0
answers
302
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
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) ...
ankitgupta.1729
397
views
ankitgupta.1729
asked
Apr 11, 2023
Mathematical Logic
testsbyankitg-dm-1
mathematical-logic
propositional-logic
2-marks
+
–
3
votes
1
answer
303
Discrete Mathematics | Propositional Logic | Test 1 | Question: 10
Consider the following two statements: i. Sentence $\textit{Neither A nor B}$ can be represented by $A \downarrow B$ where $\downarrow$ is used in Boolean circuits for $\textit{nor}$ function. ii. Sentence $\textit{not at once A and B}$ ... $(i)$ is correct Only $(ii)$ is correct Both $(i)$ and $(ii)$ are correct None of the above
Consider the following two statements: i. Sentence $\textit{Neither A nor B}$ can be represented by $A \downarrow B$ where $\downarrow$ is used in Boolean circui...
ankitgupta.1729
202
views
ankitgupta.1729
asked
Apr 11, 2023
Mathematical Logic
testsbyankitg-dm-1
mathematical-logic
propositional-logic
2-marks
+
–
5
votes
1
answer
304
Discrete Mathematics | Propositional Logic | Test 1 | Question: 11
A function $f:\{0,1\}^n \rightarrow \{0,1\}$ is called an $\textit{n-ary Boolean function}$ or $\textit{truth function}.$ We denote their totality by the set $\mathbf{B_n}.$ Now, $f \in \mathbf{B_n}$ is called $\textit{linear}$ ... of $\textit{n-ary linear Boolean functions}$ is: $2^{2^n}$ $2^{2^{n+1}}$ $2^n$ $2^{n+1}$
A function $f:\{0,1\}^n \rightarrow \{0,1\}$ is called an $\textit{n-ary Boolean function}$ or $\textit{truth function}.$ We denote their totality by the set $\m...
ankitgupta.1729
481
views
ankitgupta.1729
asked
Apr 11, 2023
Mathematical Logic
testsbyankitg-dm-1
mathematical-logic
propositional-logic
2-marks
+
–
6
votes
0
answers
305
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.
The atomic propositional variables $p_0,p_1,...$ are $\textit{formulas},$ called $\textit{prime formulas},$ also called $\textit{atomic}$ formulas, or simply $\textit{pri...
ankitgupta.1729
534
views
ankitgupta.1729
asked
Apr 11, 2023
Mathematical Logic
testsbyankitg-dm-1
mathematical-logic
propositional-logic
multiple-selects
2-marks
+
–
2
votes
1
answer
306
Discrete Mathematics | Propositional Logic | Test 1 | Question: 13
The set of logical symbols of a propositional language is called the $\textit{logical signature}.$ A logical signature is called $\textit{functionally complete}$ if every Boolean function is representable by a formula in this ... $\{\rightarrow\}$ is $\textit{not}$ functionally complete.
The set of logical symbols of a propositional language is called the $\textit{logical signature}.$ A logical signature is called $\textit{functionally complete}$ if every...
ankitgupta.1729
295
views
ankitgupta.1729
asked
Apr 11, 2023
Mathematical Logic
testsbyankitg-dm-1
mathematical-logic
propositional-logic
multiple-selects
2-marks
+
–
4
votes
1
answer
307
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 ______
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...
ankitgupta.1729
330
views
ankitgupta.1729
asked
Apr 11, 2023
Mathematical Logic
testsbyankitg-dm-1
numerical-answers
mathematical-logic
propositional-logic
2-marks
+
–
3
votes
2
answers
308
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$
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...
ankitgupta.1729
434
views
ankitgupta.1729
asked
Apr 11, 2023
Mathematical Logic
testsbyankitg-dm-1
mathematical-logic
propositional-logic
multiple-selects
2-marks
+
–
4
votes
2
answers
309
GO Classes CS 2025 | Weekly Quiz 3 | Propositional Logic | Question: 1
Let $p,q$ be two atomic propositional assertions. Then which of the following is/are false? $(p \rightarrow q) \vee (p \rightarrow \neg q)$ is a tautology. $(p \rightarrow q) \vee (q \rightarrow p)$ ... $(p \rightarrow q) \vee (\neg q \rightarrow \neg p)$ is a tautology.
Let $p,q$ be two atomic propositional assertions. Then which of the following is/are false?$(p \rightarrow q) \vee (p \rightarrow \neg q)$ is a tautology.$(p \rightarrow ...
GO Classes
605
views
GO Classes
asked
Apr 5, 2023
Mathematical Logic
goclasses2025_cs_wq3
goclasses
mathematical-logic
propositional-logic
multiple-selects
1-mark
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9
votes
3
answers
310
GO Classes CS 2025 | Weekly Quiz 3 | Propositional Logic | Question: 2
Let’s consider the interpretation $v$ where $v(p) = F, v(q) = T, v(r) = T.$ Which of the following propositional formulas are satisfied by $v$? $(p \rightarrow \neg q) \vee \neg(r \wedge q)$ $(\neg p \vee \neg q) \rightarrow (p \vee \neg r)$ $\neg(\neg p \rightarrow \neg q) \wedge r$ $\neg (\neg p \rightarrow q \wedge \neg r)$
Let’s consider the interpretation $v$ where $v(p) = F, v(q) = T, v(r) = T.$ Which of the following propositional formulas are satisfied by $v$?$(p \rightarrow \neg q) \...
GO Classes
672
views
GO Classes
asked
Apr 5, 2023
Mathematical Logic
goclasses2025_cs_wq3
goclasses
mathematical-logic
propositional-logic
multiple-selects
1-mark
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10
votes
6
answers
311
GO Classes CS 2025 | Weekly Quiz 3 | Propositional Logic | Question: 3
Consider the following atomic propositions: $\text{R}$: It is Raining $\text{S}$ ... , and vice versa It is raining is equivalent to sonu is sick It is raining or sonu is sick but not both
Consider the following atomic propositions:$\text{R}$: It is Raining$\text{S}$: Sonu is SickWhich of the following is/are correct English Translation of the following log...
GO Classes
802
views
GO Classes
asked
Apr 5, 2023
Mathematical Logic
goclasses2025_cs_wq3
goclasses
mathematical-logic
propositional-logic
multiple-selects
1-mark
+
–
7
votes
2
answers
312
GO Classes CS 2025 | Weekly Quiz 3 | Propositional Logic | Question: 4
Consider the following arguments. $\text{Argument 1:}$ ... ? Only Argument $1$ is valid. Only Argument $2$ is valid. Both Arguments are valid. No Argument is valid.
Consider the following arguments.$\text{Argument 1:}$ Kerry errs or Myrna fails to show. If Kerry errs, then he does not break the record. Myrna fails to show. Therefore,...
GO Classes
520
views
GO Classes
asked
Apr 5, 2023
Mathematical Logic
goclasses2025_cs_wq3
goclasses
mathematical-logic
propositional-logic
1-mark
+
–
7
votes
2
answers
313
GO Classes CS 2025 | Weekly Quiz 3 | Propositional Logic | Question: 10
Let $F$ and $G$ be two propositional formula. Which of the following is/are True? $F \vee G$ is a tautology iff at least one of them is a tautology If $F \rightarrow G$ is a tautology and $F$ ... is a tautology. $(F \rightarrow G) \wedge (F \rightarrow \neg G)$ is a tautology iff $F$ is a contradiction.
Let $F$ and $G$ be two propositional formula.Which of the following is/are True?$F \vee G$ is a tautology iff at least one of them is a tautologyIf $F \rightarrow G$ is a...
GO Classes
861
views
GO Classes
asked
Apr 5, 2023
Mathematical Logic
goclasses2025_cs_wq3
goclasses
mathematical-logic
propositional-logic
multiple-selects
2-marks
+
–
4
votes
2
answers
314
GO Classes CS 2025 | Weekly Quiz 3 | Propositional Logic | Question: 6
The implies connective $\rightarrow$ is one of the stranger connectives in propositional logic. Below are a series of statements regarding implications. Which of the following statements is/are TRUE? For any propositions $P$ ... $R,$ the following statement is always true: $(P \rightarrow Q) \vee (R \rightarrow Q)$.
The “implies” connective “$\rightarrow$” is one of the stranger connectives in propositional logic. Below are a series of statements regarding implications.Which ...
GO Classes
397
views
GO Classes
asked
Apr 5, 2023
Mathematical Logic
goclasses2025_cs_wq3
goclasses
mathematical-logic
propositional-logic
multiple-selects
2-marks
+
–
11
votes
2
answers
315
GO Classes 2024 | Weekly Quiz 7 | Propositional Logic | Question: 13
Consider the following list of $137$ statements: $\left(S_1\right): $ There is exactly $1$ false statement in this list. $\left(S_2\right): $ There are exactly $2$ ... true. It is possible that more than one statement in this list is true. Exactly one statement in this list is true.
Consider the following list of $137$ statements:$\left(S_1\right): $ There is exactly $1$ false statement in this list.$\left(S_2\right): $ There are exactly $2$ false st...
GO Classes
632
views
GO Classes
asked
Apr 5, 2023
Mathematical Logic
goclasses2024_wq7
goclasses
mathematical-logic
propositional-logic
2-marks
+
–
7
votes
2
answers
316
GO Classes CS 2025 | Weekly Quiz 3 | Propositional Logic | Question: 7
Which of the following logical arguments is/are valid? $\begin{aligned} & P \rightarrow(Q \rightarrow R) \\ & \neg R \\ \therefore & \neg P \\ & \end{aligned}$ ...
Which of the following logical arguments is/are valid?$\begin{aligned} & P \rightarrow(Q \rightarrow R) \\ & \neg R \\ \therefore & \neg P \\ & \end{aligned}$$\begin{alig...
GO Classes
513
views
GO Classes
asked
Apr 5, 2023
Mathematical Logic
goclasses2025_cs_wq3
goclasses
mathematical-logic
propositional-logic
multiple-selects
2-marks
+
–
12
votes
2
answers
317
GO Classes CS 2025 | Weekly Quiz 3 | Propositional Logic | Question: 8
The Logic Problem, taken from $\text{"WFF'N PROOF, The Game of Logic"}$ has these two assumptions: "Logic is difficult or not many students like logic." "If mathematics is easy, then logic ... is not easy or logic is difficult." "Logic is not difficult or mathematics is not easy."
The Logic Problem, taken from $\text{"WFF'N PROOF, The Game of Logic"}$ has these two assumptions:"Logic is difficult or not many students like logic.""If mathematics is ...
GO Classes
525
views
GO Classes
asked
Apr 5, 2023
Mathematical Logic
goclasses2025_cs_wq3
goclasses
mathematical-logic
propositional-logic
multiple-selects
2-marks
+
–
22
votes
6
answers
318
GO Classes CS 2025 | Weekly Quiz 3 | Propositional Logic | Question: 9
Which of the following statements is/are true? The argument form with premises $p_1, p_2, \ldots, p_n$ and conclusion $q \rightarrow r$ is valid iff the argument form with premises $p_1, p_2, \ldots, p_n, r$ ... the argument form with premises $p_1, p_2, \ldots, p_n, \sim r$, and conclusion $\sim q$ is valid.
Which of the following statements is/are true?The argument form with premises $p_1, p_2, \ldots, p_n$ and conclusion $q \rightarrow r$ is valid iff the argument form with...
GO Classes
1.4k
views
GO Classes
asked
Apr 5, 2023
Mathematical Logic
goclasses2025_cs_wq3
goclasses
mathematical-logic
propositional-logic
multiple-selects
2-marks
+
–
0
votes
1
answer
319
Flamingos Fanny and Freddy have three offspring: Happy, Glee, and Joy. These five flamingos are to be distributed to seven different zoos so that no zoo gets both a parent and a child :(. It is not required that every zoo gets a flamingo. In how many different ways can this be done? here if i am using case method on children i am getting a different answer than when i am using case methon on parents, why is that?
Soujit
501
views
Soujit
asked
Apr 5, 2023
Combinatory
combinatory
+
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0
votes
1
answer
320
Discrete-mathematics | Mathematical-logic
Which of the following predicate is/are valid? S1: $\forall x(A(x)\Leftrightarrow B(x))\Rightarrow \exists x(A(x)\Rightarrow B(x))$ S2: $\exists x(A(x)\vee B(x))\Leftrightarrow (\exists xA(x)\vee\exists xB(x))$ A. only S1 B. only S2 C. Both D. None
Which of the following predicate is/are valid? S1: $\forall x(A(x)\Leftrightarrow B(x))\Rightarrow \exists x(A(x)\Rightarrow B(x))$ S2: $\exists x(A(x)\vee B(x))\Le...
Jay Patel 009
386
views
Jay Patel 009
asked
Mar 31, 2023
Mathematical Logic
discrete-mathematics
mathematical-logic
first-order-logic
virtual-gate-test-series
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