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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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Most answered questions in Mathematical Logic

3 votes
3 answers
205
Kenneth Rosen Edition 7 Exercise 1.1 Question 4 (Page No. 12)
What is the negation of each of these propositions? Jennifer and Teja are friends. There are 13 items in a baker’s dozen. Abby sent more than 100 text messages every day. 121 is a perfect square.
What is the negation of each of these propositions?Jennifer and Teja are friends.There are 13 items in a baker’s dozen.Abby sent more than 100 text messages every day.1...
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34 votes
3 answers
211
GATE CSE 2015 Set 1 | Question: 1‏4
Which one of the following is NOT equivalent to $p ↔ q$? $(\neg p ∨ q) ∧ (p ∨ \neg q)$ $(\neg p ∨ q) ∧ (q → p)$ $(\neg p ∧ q) ∨ ( p ∧ \neg q)$ $(\neg p ∧ \neg q) ∨ (p ∧ q)$
Which one of the following is NOT equivalent to $p ↔ q$?$(\neg p ∨ q) ∧ (p ∨ \neg q)$$(\neg p ∨ q) ∧ (q → p)$$(\neg p ∧ q) ∨ ( p ∧ \neg q)$$(\neg p �...
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6 votes
3 answers
212
Which of the following is a tautology?
Which of the following is a tautology? $P \rightarrow P \wedge Q$ $P \rightarrow Q \wedge V$ $(P \rightarrow Q) \wedge (Q \rightarrow R) \rightarrow P \rightarrow R$ $(P \rightarrow Q) \leftrightarrow (\sim Q \rightarrow \sim P)$
Which of the following is a tautology?$P \rightarrow P \wedge Q$$P \rightarrow Q \wedge V$$(P \rightarrow Q) \wedge (Q \rightarrow R) \rightarrow P \rightarrow R$$(P \rig...
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22 votes
3 answers
213
GATE CSE 1995 | Question: 13
Obtain the principal (canonical) conjunctive normal form of the propositional formula $(p \wedge q) \vee (\neg q \wedge r)$ where $\wedge$ is logical and, $\vee$ is inclusive or and $\neg$ is negation.
Obtain the principal (canonical) conjunctive normal form of the propositional formula $$(p \wedge q) \vee (\neg q \wedge r)$$ where $\wedge$ is logical and, $\vee$ is inc...
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22 votes
3 answers
214
GATE CSE 1994 | Question: 3.13
Let $p$ and $q$ be propositions. Using only the Truth Table, decide whether $p \Longleftrightarrow q$ does not imply $p \to \lnot q$ is True or False.
Let $p$ and $q$ be propositions. Using only the Truth Table, decide whether $p \Longleftrightarrow q$ does not imply $p \to \lnot q$is True or False.
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18 votes
3 answers
215
GATE CSE 1993 | Question: 18
Show that proposition $C$ is a logical consequence of the formula$A\wedge \left(A \to \left(B \vee C\right)\right) \wedge \left( B \to \neg A\right)$using truth tables.
Show that proposition $C$ is a logical consequence of the formula$$A\wedge \left(A \to \left(B \vee C\right)\right) \wedge \left( B \to \neg A\right)$$using truth tables....
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18 votes
3 answers
216
GATE CSE 1997 | Question: 3.2
Which of the following propositions is a tautology? $(p \vee q) \rightarrow p$ $p \vee (q \rightarrow p)$ $p \vee (p \rightarrow q)$ $p \rightarrow (p \rightarrow q)$
Which of the following propositions is a tautology?$(p \vee q) \rightarrow p$$p \vee (q \rightarrow p)$$p \vee (p \rightarrow q)$$p \rightarrow (p \rightarrow q)$
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13 votes
3 answers
217
GATE CSE 1999 | Question: 14
Show that the formula $\left[(\sim p \vee q) \Rightarrow (q \Rightarrow p)\right]$ is not a tautology. Let $A$ be a tautology and $B$ any other formula. Prove that $(A \vee B)$ is a tautology.
Show that the formula $\left[(\sim p \vee q) \Rightarrow (q \Rightarrow p)\right]$ is not a tautology.Let $A$ be a tautology and $B$ any other formula. Prove that $(A \ve...
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47 votes
3 answers
219
GATE CSE 2013 | Question: 47
Which one of the following is NOT logically equivalent to $¬∃x(∀ y (α)∧∀z(β ))$ ? $∀ x(∃ z(¬β )→∀ y(α))$ $∀x(∀ z(β )→∃ y(¬α))$ $∀x(∀ y(α)→∃z(¬β ))$ $∀x(∃ y(¬α)→∃z(¬β ))$
Which one of the following is NOT logically equivalent to $¬∃x(∀ y (α)∧∀z(β ))$ ?$∀ x(∃ z(¬β )→∀ y(α))$$∀x(∀ z(β )→∃ y(¬α))$$∀x(∀ y(�...
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