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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

0 votes
1 answer
1
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 in Mathematical Logic Lakshman Patel RJIT 88 views
0 votes
2 answers
2
1 vote
2 answers
3
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 in Mathematical Logic Lakshman Patel RJIT 128 views
0 votes
2 answers
4
0 votes
3 answers
5
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 in Mathematical Logic Lakshman Patel RJIT 273 views
0 votes
1 answer
6
The proposition ~ q ∨ p is equivalent to :
asked Mar 27 in Mathematical Logic jothee 77 views
0 votes
2 answers
7
0 votes
1 answer
8
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 in Mathematical Logic jothee 228 views
7 votes
4 answers
9
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 in Mathematical Logic Arjun 2.8k views
9 votes
5 answers
10
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 in Mathematical Logic Arjun 3.5k views
5 votes
3 answers
11
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 in Mathematical Logic Arjun 2.3k views
5 votes
3 answers
12
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 in Mathematical Logic Satbir 705 views
1 vote
1 answer
13
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 169 views
4 votes
3 answers
14
Which of the following is principal conjunctive normal form for $[(p\vee q)\wedge\ \rceil p \rightarrow \rceil q ]$ ? $p\ \vee \rceil q$ $p \vee q $ $\rceil p \vee q$ $\rceil p\ \vee \rceil q$
asked Jul 2, 2019 in Mathematical Logic Arjun 1.4k views
5 votes
3 answers
15
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 680 views
3 votes
1 answer
16
“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 313 views
2 votes
1 answer
17
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 149 views
1 vote
1 answer
18
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 227 views
1 vote
0 answers
19
A women's health clinic has four doctors and each patient is assigned to one of them. If a patient givs birth btween 8 am and 4 pm, then her chance of being attended by her assigned doctor is 3/4, otherwise it is 1/4. What is the probability that a patient is attended by the assigned doctor when she gives birth? (A) 25/144 (B) 5/12 (C) 7/12 (D) 1/12
asked May 30, 2019 in Mathematical Logic JAYKISHAN 280 views
0 votes
1 answer
20
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