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Syllabus: Propositional and first order logic.

$$\scriptsize{\overset{{\large{\textbf{Mark Distribution in Previous GATE}}}}{\begin{array}{|c|c|c|c|c|c|c|c|}\hline
\textbf{Year}&\textbf{2024-1}&\textbf{2024-2}&\textbf{2023}& \textbf{2022}& \textbf{2021-1}&\textbf{2021-2}&\textbf{Minimum}&\textbf{Average}&\textbf{Maximum}
\\\hline\textbf{1 Mark Count}&0&1&1& 0 & 1&1&0&0.67&1
\\\hline\textbf{2 Marks Count}&0&0&0&0 & 0&0&0&0&0
\\\hline\textbf{Total Marks}& 0&1&1& 0 & 1&1&\bf{0}&\bf{0.67}&\bf{1}\\\hline
\end{array}}}$$

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Recent questions in Mathematical Logic

#141
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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 ... $P \vee Q$ $P \vee \neg P$
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#142
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1 answers
2 votes
Discrete Mathematics | Propositional Logic | Test 1 | Question: 6
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 ... ) are correct (i),(ii) and (iv) are correct
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#143
732
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0 answers
6 votes
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- ... Q and R are atomic propositions) Total number of well-formed formulas are ______
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#144
289
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1 answers
3 votes
Discrete Mathematics | Propositional Logic | Test 1 | Question: 8
Consider the following truth table for the connective $\rightarrow:$ ... correct         (i) and (ii) are correct         (i), (ii) and (iii) are correct
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#145
422
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0 answers
2 votes
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) ... and $(iii)$ are correct           $(i),(ii)$ and $(iii)$ are correct
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#146
229
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1 answers
3 votes
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 ... Both $(i)$ and $(ii)$ are correct None of the above
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#147
543
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1 answers
5 votes
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 $\mathbf{B_n}.$ ... $2^n$ $2^{n+1}$
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#148
573
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0 answers
6 votes
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 $\textit{primes}.$ ... $p \vee \neg (\neg p \wedge q)$ is either a DNF or a CNF.
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#149
315
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1 answers
2 votes
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 $\textit{functionally complete}$ ... The signature $\{\rightarrow\}$ is $\textit{not}$ functionally complete.
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#150
368
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1 answers
4 votes
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 ... is a tautology Number of correct statements are ______
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#151
467
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2 answers
3 votes
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 ... $P \rightarrow Q$ $\neg P \wedge Q$
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#152
763
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2 answers
5 votes
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?$(p \rightarrow q) \vee (p \rightarrow \neg q)$ ... .$(p \rightarrow q) \vee (\neg q \rightarrow \neg p)$ is a tautology.
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#153
841
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3 answers
9 votes
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) \wedge r$\neg (\neg p \rightarrow q \wedge \neg r)$
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#154
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6 answers
10 votes
GO Classes CS 2025 | Weekly Quiz 3 | Propositional Logic | Question: 3
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 ... is equivalent to sonu is sickIt is raining or sonu is sick but not both
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#155
672
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2 answers
7 votes
GO Classes CS 2025 | Weekly Quiz 3 | Propositional Logic | Question: 4
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 ... valid.Only Argument $2$ is valid.Both Arguments are valid.No Argument is valid.
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#156
1.1k
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2 answers
8 votes
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?$F \vee G$ ... $F$ is a contradiction.
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#157
497
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2 answers
5 votes
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 ... always true: $(P \rightarrow Q) \vee (R \rightarrow Q)$.
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#158
703
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2 answers
11 votes
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 ... than one statement in this list is true.Exactly one statement in this list is true.
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#159
637
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2 answers
8 votes
GO Classes CS 2025 | Weekly Quiz 3 | Propositional Logic | Question: 7
Which of the following logical arguments is/are valid?$\begin{aligned} & P \rightarrow(Q \rightarrow R) \\ & \neg R \\ \therefore & \neg P \\ & \end{aligned}$\begin{ ...
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#160
699
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2 answers
12 votes
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 ... easy or logic is difficult.""Logic is not difficult or mathematics is not easy."
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