Recent questions and answers in Mathematical Logic - GATE Overflow

+19 votes

5 answers

1

GATE2009-24
The binary operation $\Box$ ... of the following is equivalent to $P \vee Q$? $\neg Q \Box \neg P$ $P\Box \neg Q$ $\neg P\Box Q$ $\neg P\Box \neg Q$

answered 5 days ago in Mathematical Logic by abichandani | 2.6k views

+27 votes

4 answers

2

GATE1991-15,b
Consider the following first order formula: ... Does it have finite models? Is it satisfiable? If so, give a countable model for it.

answered Jul 3 in Mathematical Logic by Deepakk Poonia (Dee) | 2.2k views

+45 votes

5 answers

3

GATE2016-2-27
Which one of the following well-formed formulae in predicate calculus is NOT valid ? $(\forall _{x} p(x) \implies \forall _{x} q(x)) \implies (\exists _{x} \neg p(x) \vee \forall _{x} q(x))$ $(\exists x p(x) \vee \exists x q (x)) \implies \exists x (p(x) \vee q (x))$ ... $\forall x (p(x) \vee q(x)) \implies (\forall x p(x) \vee \forall x q(x))$

answered Jul 3 in Mathematical Logic by Kushagra गुप्ता | 7k views

+29 votes

9 answers

4

GATE2014-1-53
Which one of the following propositional logic formulas is TRUE when exactly two of $p,q$ and $r$ are TRUE? $(( p \leftrightarrow q) \wedge r) \vee (p \wedge q \wedge \sim r)$ $( \sim (p \leftrightarrow q) \wedge r)\vee (p \wedge q \wedge \sim r)$ $( (p \to q) \wedge r) \vee (p \wedge q \wedge \sim r)$ $(\sim (p \leftrightarrow q) \wedge r) \wedge (p \wedge q \wedge \sim r) $

answered Jul 2 in Mathematical Logic by Kushagra गुप्ता | 4.1k views

+2 votes

1 answer

5

J.P TREMBLAY EXCERCISE 1-4.1 4 TH QUESTION

answered Jul 1 in Mathematical Logic by ubibhatt | 200 views

+3 votes

2 answers

6

PREDICATE LOGIC
Recall that a predicate logic statement is contingent if its truth value depends on the choice of the universe and on the interpretations of the predicate symbol $S$ and the constant symbol $b$ involved. Consider the following predicate logic statements in ... . Always true - Contingent - Always false. Always true - Contingent - Contingent. Contingent - Always true - Always false.

answered Jun 17 in Mathematical Logic by Deepakk Poonia (Dee) | 206 views

+10 votes

6 answers

7

GATE1989-3-v
Answer the following: Which of the following well-formed formulas are equivalent? $P \rightarrow Q$ $\neg Q \rightarrow \neg P$ $\neg P \vee Q$ $\neg Q \rightarrow P$

answered May 31 in Mathematical Logic by iwasifirshad | 854 views

+1 vote

1 answer

8

CMI2019-B-5
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 ... $3:$ My lawyer always tells the truth. Which of the above suspects are innocent, and which are guilty? Explain your reasoning.

answered May 28 in Mathematical Logic by Mohit Kumar 6 | 123 views

+1 vote

1 answer

9

floyd warshall algo
unable to understand

answered May 11 in Mathematical Logic by crystal shadow | 357 views

0 votes

1 answer

10

NIELIT 2016 MAR Scientist C - Section B: 10
$\underset{x \rightarrow 0}{\lim} \dfrac{x^{3}+x^{2}-5x-2}{2x^{3}-7x^{2}+4x+4}=?$ $-0.5$ $(0.5)$ $\infty$ None of the above

answered May 3 in Mathematical Logic by Mohit Kumar 6 | 15 views

+4 votes

3 answers

11

ISRO2020-73
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

answered Apr 30 in Mathematical Logic by DIBAKAR MAJEE | 497 views

+49 votes

9 answers

12

GATE2015-3-24
In a room there are only two types of people, namely $\text{Type 1}$ and $\text{Type 2}$. $\text{Type 1}$ people always tell the truth and $\text{Type 2}$ people always lie. You give a fair coin to a person in that room, without knowing which type he is from ... If the person is of $\text{Type 2}$, then the result is tail If the person is of $\text{Type 1}$, then the result is tail

answered Apr 13 in Mathematical Logic by Lakshman Patel RJIT | 6.3k views

+5 votes

3 answers

13

UGCNET-June-2019-II: 8
Match List-I with List-II: ... - (iv); (b) - (i); (c) - (iii); (d) - (ii) (a) - (iv); (b) - (iii); (c) - (i); (d) - (ii)

answered Apr 5 in Mathematical Logic by immanujs | 391 views

+4 votes

3 answers

14

UGCNET-June-2019-II: 6
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 $ $\rceil p \vee q$ $\rceil p\ \vee \rceil q$

answered Apr 5 in Mathematical Logic by immanujs | 666 views

0 votes

1 answer

15

NIELIT 2016 MAR Scientist C - Section B: 8
The eigenvalues of the matrix $\begin{bmatrix}1 & 2\\ 4 & 3 \end{bmatrix}$ are $\text{5 and -5}$ $\text{5 and -1}$ $\text{1 and -5}$ $\text{2 and 3}$

answered Apr 5 in Mathematical Logic by gaurav1.yuva | 20 views

0 votes

1 answer

16

NIELIT 2016 MAR Scientist C - Section B: 4
If $A$ and $B$ are two related events, and $P(A \mid B)$ represents the conditional probability, Bayes’ theorem states that $P(A\mid B) = \dfrac{P(A)}{P(B)} P(B\mid A)$ $P(A\mid B) = P(A) P(B) P(B\mid A)$ $P(A\mid B) = \dfrac{P(A)}{P(B)}$ $P(A\mid B) = P(A)+P(B)$

answered Apr 5 in Mathematical Logic by gaurav1.yuva | 30 views

0 votes

1 answer

17

NIELIT 2016 MAR Scientist C - Section B: 20
Degree of each vertex in $K_n$ is $n$ $n-1$ $n-2$ $2n-1$

answered Apr 4 in Mathematical Logic by Vipin Tiwari | 24 views

0 votes

2 answers

18

NIELIT 2017 July Scientist B (CS) - Section B: 16
Which of the following propositions is tautology? $(p\lor q)\to q$ $p\lor (q\to p)$ $p\lor (p\to q)$ Both (B) and (C)

answered Apr 3 in Mathematical Logic by smsubham | 35 views

0 votes

1 answer

19

NIELIT 2017 July Scientist B (IT) - Section B: 13
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 $Q\lor P$ ... $(P\land Q)\lor(\sim P\land Q)\lor (P \land \sim Q)$ is equal to $P\lor (Q\land \sim P)$

answered Apr 3 in Mathematical Logic by immanujs | 22 views

0 votes

1 answer

20

NIELIT 2016 MAR Scientist C - Section B: 11
$\displaystyle \int_{0}^{\dfrac{\pi}{2}} \sin^{7}\theta \cos ^{4} \theta d\theta=?$ $16/1155$ $16/385$ $16\pi/385$ $8\pi/385$

answered Apr 3 in Mathematical Logic by Vipin Tiwari | 17 views

+1 vote

0 answers

21

NIELIT 2016 MAR Scientist C - Section B: 1
Choose the most appropriate option. The Newton-Raphson iteration $x_{n+1}=\dfrac{x_{n}}{2}+\dfrac{3}{2x_{n}}$ can be used to solve the equation $x^{2}=3$ $x^{3}=3$ $x^{2}=2$ $x^{3}=2$

asked Apr 2 in Mathematical Logic by Lakshman Patel RJIT | 47 views

+1 vote

0 answers

22

NIELIT 2016 MAR Scientist C - Section B: 6
If $y=f(x)$, in the interval $[a,b]$ is rotated about the $x$-axis, the Volume of the solid of revolution is $(f’(x)=dy/dx)$ $\int_{a}^{b} \pi [f(x)]^{2} dx \\$ $\int_{a}^{b}[f(x)]^{3} dx \\$ $\int_{a}^{b} \pi [{f}'(x)]^{2} dx \\$ $\int_{a}^{b} \pi^{2} f(x)dx \\$

asked Apr 2 in Mathematical Logic by Lakshman Patel RJIT | 14 views

0 votes

0 answers

23

NIELIT 2016 MAR Scientist C - Section B: 7
The area under the curve $y(x)=3e^{-5x}$ from $x=0 \text{ to } x=\infty$ is $\dfrac{3}{5}$ $\dfrac{-3}{5}$ ${5}$ $\dfrac{5}{3}$

asked Apr 2 in Mathematical Logic by Lakshman Patel RJIT | 17 views

0 votes

0 answers

24

NIELIT 2016 MAR Scientist C - Section B: 9
Consider three vectors $x=\begin{bmatrix}1\\2 \end{bmatrix}, y=\begin{bmatrix}4\\8 \end{bmatrix},z=\begin{bmatrix}3\\1 \end{bmatrix}$. Which of the folowing statements is true $x$ and $y$ are linearly independent $x$ and $y$ are linearly dependent $x$ and $z$ are linearly dependent $y$ and $z$ are linearly dependent

asked Apr 2 in Mathematical Logic by Lakshman Patel RJIT | 18 views

0 votes

0 answers

25

NIELIT 2016 MAR Scientist C - Section B: 12
$\displaystyle \lim_{x \rightarrow a}\frac{1}{x^{2}-a^{2}} \displaystyle \int_{a}^{x}\sin (t^{2})dt=$? $2a \sin (a^{2})$ $2a$ $\sin (a^{2})$ None of the above

asked Apr 2 in Mathematical Logic by Lakshman Patel RJIT | 12 views

0 votes

0 answers

26

NIELIT 2016 MAR Scientist C - Section B: 14
Find the area bounded by the curve $y=\sqrt{5-x^{2}}$ and $y=\mid x-1 \mid$ $\dfrac{2}{0}(2\sqrt{6}-\sqrt{3})-\dfrac{5}{2}$ $\dfrac{2}{3}(6\sqrt{6}+3\sqrt{3})+\dfrac{5}{2}$ $2(\sqrt{6}-\sqrt{3})-5$ $\dfrac{2}{3}(\sqrt{6}-\sqrt{3})+5$

asked Apr 2 in Mathematical Logic by Lakshman Patel RJIT | 14 views

0 votes

0 answers

27

NIELIT 2016 MAR Scientist C - Section B: 15
The equation of the plane through the point $(-1,3,2)$ and perpendicular to each of the planes $x+2y+3z=5$ and $3x+3y+z=0$ is $7x-8y+3z+25=0$ $7x+8y+3z+25=0$ $7x-8y+3z-25=0$ $7x-8y-3z-25=0$

asked Apr 2 in Mathematical Logic by Lakshman Patel RJIT | 12 views

0 votes

0 answers

28

NIELIT 2016 MAR Scientist C - Section B: 16
Evaluate the sum $S=1+1+\dfrac{3}{2^{2}}+\dfrac{3}{2^{3}}+\dfrac{5}{2^{4}}+\dots$ $1$ $2$ $3$ $4$

asked Apr 2 in Mathematical Logic by Lakshman Patel RJIT | 21 views

0 votes

0 answers

29

NIELIT 2016 MAR Scientist C - Section B: 17
A ladder $13$ feet long rests against the side of a house. The bottom of the ladder slides away from the house at a rate of $0.5$ ft/s. How fast is the top of the ladder sliding down the wall when the bottom of the ladder is $5$ ... $-\dfrac{5}{24} \text {ft/s} \\$ $-\dfrac{5}{12} \text{ ft/s}$

asked Apr 2 in Mathematical Logic by Lakshman Patel RJIT | 13 views

0 votes

0 answers

30

NIELIT 2016 MAR Scientist C - Section B: 18
Find the volume of the solid obtained by rotating the region bound by the curves $y=x^3+1, \: x=1$, and $y=0$ about the $x$-axis $\dfrac{23\pi}{7} \\$ $\dfrac{16\pi}{7} \\$ $2\pi \\$ $\dfrac{19\pi}{7}$

asked Apr 2 in Mathematical Logic by Lakshman Patel RJIT | 13 views

0 votes

0 answers

31

NIELIT 2016 MAR Scientist C - Section B: 19
If product of matrix $A=\begin{bmatrix}\cos^{2}\theta &\cos \theta \sin \theta \\ \cos \theta \sin \theta &\sin ^{2} \theta& \end{bmatrix}$ ... by an odd multiple of $\pi$ even multiple of $\pi$ odd multiple of $\dfrac{\pi}{2}$ even multiple of $\dfrac{\pi}{2}$

asked Apr 2 in Mathematical Logic by Lakshman Patel RJIT | 16 views

0 votes

1 answer

32

UGCNET-Dec2006-II: 2
The proposition ~ q ∨ p is equivalent to :

answered Apr 2 in Mathematical Logic by immanujs | 45 views

0 votes

2 answers

33

NIELIT 2017 DEC Scientist B - Section B: 43
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 by Lakshman Patel RJIT | 58 views

0 votes

2 answers

34

UGCNET-Jan2017-II: 2
Match the following : ...

asked Mar 24 in Mathematical Logic by jothee | 75 views

0 votes

1 answer

35

UGCNET-Jan2017-II: 6
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 by jothee | 69 views

+5 votes

3 answers

36

GATE2020-CS-45
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______________

answered Mar 18 in Mathematical Logic by felics moses 1 | 1.3k views

+1 vote

2 answers

37

MadeEasy Test Series: Mathematical Logic - First Order Logic
Pardon for the screenshot though. No idea of latex.

answered Mar 2 in Mathematical Logic by Madhab | 363 views

+7 votes

4 answers

38

GATE2020-CS-1
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

answered Feb 27 in Mathematical Logic by immanujs | 2k views

+35 votes

8 answers

39

GATE2002-1.8
"If $X$ then $Y$ unless $Z$" is represented by which of the following formulas in prepositional logic? ("$\neg$" is negation, "$\land$" is conjunction, and "$\rightarrow$" is implication) $(X\land \neg Z) \rightarrow Y$ $(X \land Y) \rightarrow \neg Z$ $X \rightarrow(Y\land \neg Z)$ $(X \rightarrow Y)\land \neg Z$

answered Feb 26 in Mathematical Logic by Pratyush Priyam Kuan | 5.6k views

+32 votes

5 answers

40

GATE2000-2.7
Let $a, b, c, d$ be propositions. Assume that the equivalence $a ⇔ ( b \vee \neg b)$ and $b ⇔c$ hold. Then the truth-value of the formula $(a ∧ b) → (a ∧ c) ∨ d$ is always True False Same as the truth-value of $b$ Same as the truth-value of $d$

answered Feb 26 in Mathematical Logic by Pratyush Priyam Kuan | 3.1k views

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