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Syllabus: Propositional and first order logic.

$$\small{\overset{{\large{\textbf{Mark Distribution in Previous GATE}}}}{\begin{array}{|c|c|c|c|c|c|c|c|}\hline
\textbf{Year}&\textbf{2019}&\textbf{2018}&\textbf{2017-1}&\textbf{2017-2}&\textbf{2016-1}&\textbf{2016-2}&\textbf{Minimum}&\textbf{Average}&\textbf{Maximum}
\\\hline\textbf{1 Mark Count}&0&0&2&1&1&1&0&0.8&2
\\\hline\textbf{2 Marks Count}&1&1&1&0&0&1&0&0.7&1
\\\hline\textbf{Total Marks}&2&2&4&1&1&3&\bf{1}&\bf{2.2}&\bf{4}\\\hline
\end{array}}}$$

Recent questions in Mathematical Logic

2 votes
2 answers
1
Choose the correct choice(s) regarding the following proportional logic assertion $S$: $S: (( P \wedge Q) \rightarrow R) \rightarrow (( P \wedge Q) \rightarrow (Q \rightarrow R))$ $S$ is neither a tautology nor a contradiction $S$ is a tautology $S$ is a contradiction The antecedent of $S$ is logically equivalent to the consequent of $S$
asked Feb 18 in Mathematical Logic Arjun 346 views
0 votes
4 answers
2
Let $p$ and $q$ be two propositions. Consider the following two formulae in propositional logic. $S_1: (\neg p\wedge(p\vee q))\rightarrow q$ $S_2: q\rightarrow(\neg p\wedge(p\vee q))$ Which one of the following choices is correct? Both $S_1$ and $S_2$ are tautologies ... tautology but $S_2$ is not a tautology $S_1$ is not a tautology but $S_2$ is a tautology Niether $S_1$ nor $S_2$ is a tautology
asked Feb 18 in Mathematical Logic Arjun 204 views
0 votes
2 answers
3
Which of the following is FALSE? $Read\ \wedge as\ AND, \vee\ as\ OR, \sim as\ NOT, \rightarrow$ as one way implication and $\leftrightarrow$ as two way implication? $((x\rightarrow y)\wedge x)\rightarrow y$ $((\sim x\rightarrow y)\wedge (\sim x\wedge \sim y))\rightarrow x$ $(x\rightarrow (x\vee y))$ $((x\vee y)\leftrightarrow (\sim x\vee \sim y))$
asked Apr 2, 2020 in Mathematical Logic Lakshman Patel RJIT 127 views
0 votes
4 answers
4
1 vote
3 answers
5
Which of the following statements is false? $(P\land Q)\lor(\sim P\land Q)\lor(P \land \sim Q)$ is equal to $\sim Q\land \sim P$ $(P\land Q)\lor(\sim P\land Q)\lor(P \wedge \sim Q)$ is equal to $Q\lor P$ $(P\wedge Q)\lor (\sim P\land Q)\lor(P \wedge \sim Q)$ is equal to $Q\lor (P\wedge \sim Q)$ $(P\land Q)\lor(\sim P\land Q)\lor (P \land \sim Q)$ is equal to $P\lor (Q\land \sim P)$
asked Mar 30, 2020 in Mathematical Logic Lakshman Patel RJIT 183 views
0 votes
3 answers
6
0 votes
3 answers
7
Which one is the correct translation of the following statement into mathematical logic? “None of my friends are perfect.” $\neg\:\exists\:x(p(x)\land q(x))$ $\exists\:x(\neg\:p(x)\land q(x))$ $\exists\:x(\neg\:p(x)\land\neg\:q(x))$ $\exists\:x(p(x)\land\neg\:q(x))$
asked Mar 30, 2020 in Mathematical Logic Lakshman Patel RJIT 370 views
0 votes
1 answer
8
The proposition ~ q ∨ p is equivalent to :
asked Mar 27, 2020 in Mathematical Logic jothee 109 views
0 votes
3 answers
9
0 votes
2 answers
10
In propositional logic if $\left ( P \rightarrow Q \right )\wedge \left ( R \rightarrow S \right )$ and $\left ( P \vee R \right )$ are two premises such that $\begin{array}{c} (P \to Q) \wedge (R \to S) \\ P \vee R \\ \hline Y \\ \hline \end{array}$ $Y$ is the premise : $P \vee R$ $P \vee S$ $Q \vee R$ $Q \vee S$
asked Mar 24, 2020 in Mathematical Logic jothee 329 views
11 votes
4 answers
11
Consider the functions $e^{-x}$ $x^{2}-\sin x$ $\sqrt{x^{3}+1}$ Which of the above functions is/are increasing everywhere in $[ 0,1]$? Ⅲ only Ⅱ only Ⅱ and Ⅲ only Ⅰ and Ⅲ only
asked Feb 12, 2020 in Mathematical Logic Arjun 5.2k views
13 votes
5 answers
12
Which one of the following predicate formulae is NOT logically valid? Note that $W$ is a predicate formula without any free occurrence of $x$. $\forall x (p(x) \vee W) \equiv \forall x \: ( px) \vee W$ $\exists x(p(x) \wedge W) \equiv \exists x \: p(x) \wedge W$ ... $\exists x(p(x) \rightarrow W) \equiv \forall x \: p(x) \rightarrow W$
asked Feb 12, 2020 in Mathematical Logic Arjun 5.5k views
8 votes
3 answers
13
For $n>2$, let $a \in \{0,1\}^n$ be a non-zero vector. Suppose that $x$ is chosen uniformly at random from $\{0,1\}^n$. Then, the probability that $\displaystyle{} \Sigma_{i=1}^n a_i x_i$ is an odd number is______________
asked Feb 12, 2020 in Mathematical Logic Arjun 4.8k views
5 votes
3 answers
14
Given that $B(a)$ means “$a$ is a bear” $F(a)$ means “$a$ is a fish” and $E(a,b)$ means “$a $ eats $b$” Then what is the best meaning of $\forall x [F(x) \to \forall y(E(y,x)\rightarrow b(y))]$ Every fish is eaten by some bear Bears eat only fish Every bear eats fish Only bears eat fish
asked Jan 13, 2020 in Mathematical Logic Satbir 841 views
1 vote
1 answer
15
In the land of Twitter, there are two kinds of people: knights (also called outragers), who always tell the truth, and knaves (also called trolls), who always lie. It so happened that a person with handle @anand tweeted something offensive. It was not known ... Suspect $3:$ My lawyer always tells the truth. Which of the above suspects are innocent, and which are guilty? Explain your reasoning.
asked Sep 13, 2019 in Mathematical Logic gatecse 204 views
4 votes
3 answers
16
Which of the following is principal conjunctive normal form for $[(p\vee q)\wedge\ \neg p \rightarrow \neg q ]$ ? $p\ \vee \neg q$ $p \vee q $ $\neg p \vee q$ $\neg p\ \vee \neg q$
asked Jul 2, 2019 in Mathematical Logic Arjun 1.7k views
5 votes
4 answers
17
Match List-I with List-II: ... - (iv) (a) - (iv); (b) - (i); (c) - (iii); (d) - (ii) (a) - (iv); (b) - (iii); (c) - (i); (d) - (ii)
asked Jul 2, 2019 in Mathematical Logic Arjun 769 views
3 votes
1 answer
18
“Not every satisfiable logic is valid” Representation of it will be $1)\sim \left ( \forall S(x)\rightarrow V(x) \right )$ or $2)\sim \left ( \forall S(x)\vee V(x) \right )$ Among $1)$ and $2)$, which one is correct? and why?
asked Jun 4, 2019 in Mathematical Logic srestha 370 views
2 votes
1 answer
19
Read the statements: All women are entrepreneurs. Some women are doctors. Which of the following conclusions can be logically inferred from the above statements? All women are doctors All doctors are entrepreneurs All entrepreneurs are women Some entrepreneurs are doctors Why here $2)$ ... ans?? Is it because , if we make set of doctor as 0, then All doctors are entrepreneurs is meaningless.
asked Jun 1, 2019 in Mathematical Logic srestha 174 views
1 vote
1 answer
20
The notation $\exists ! x P(x)$ denotes the proposition “there exists a unique $x$ such that $P(x)$ is true”. Give the truth values of the following statements : I)${\color{Red} {\exists ! x P(x)}} \rightarrow \exists x P(x)$ II)${\color{Red} {\exists ! x\sim P(x)}} \rightarrow \neg \forall x P(x)$ What will be answer here?? Is the assumption only for left hand side and not right hand side??
asked May 31, 2019 in Mathematical Logic srestha 275 views
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