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Recent questions and answers in Mathematical Logic
+19
votes
5
answers
1
GATE200924
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
gate2009
mathematicallogic
easy
propositionallogic
+27
votes
4
answers
2
GATE199115,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
gate1991
firstorderlogic
descriptive
+45
votes
5
answers
3
GATE2016227
Which one of the following wellformed 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
gate20162
mathematicallogic
firstorderlogic
normal
+29
votes
9
answers
4
GATE2014153
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
gate20141
mathematicallogic
normal
propositionallogic
+2
votes
1
answer
5
J.P TREMBLAY EXCERCISE 14.1 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
GATE19893v
Answer the following: Which of the following wellformed 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
gate1989
normal
mathematicallogic
propositionallogic
+1
vote
1
answer
8
CMI2019B5
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
cmi2019
mathematicallogic
logicalreasoning
descriptive
+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
$\underset{x \rightarrow 0}{\lim} \dfrac{x^{3}+x^{2}5x2}{2x^{3}7x^{2}+4x+4}=?$ $0.5$ $(0.5)$ $\infty$ None of the above
answered
May 3
in
Mathematical Logic
by
Mohit Kumar 6

15
views
nielit2016marscientistc
+4
votes
3
answers
11
ISRO202073
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
isro2020
discretemathematics
mathematicallogic
propositionallogic
normal
+49
votes
9
answers
12
GATE2015324
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
gate20153
mathematicallogic
difficult
logicalreasoning
+5
votes
3
answers
13
UGCNETJune2019II: 8
Match ListI with ListII: ...  (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
ugcnetjune2019ii
propositionallogic
+4
votes
3
answers
14
UGCNETJune2019II: 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
ugcnetjune2019ii
propositionallogic
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
nielit2016marscientistc
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
nielit2016marscientistc
0
votes
1
answer
17
NIELIT 2016 MAR Scientist C  Section B: 20
Degree of each vertex in $K_n$ is $n$ $n1$ $n2$ $2n1$
answered
Apr 4
in
Mathematical Logic
by
Vipin Tiwari

24
views
nielit2016marscientistc
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
nielit2017julyscientistbcs
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
nielit2017julyscientistbit
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
nielit2016marscientistc
+1
vote
0
answers
21
NIELIT 2016 MAR Scientist C  Section B: 1
Choose the most appropriate option. The NewtonRaphson 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
nielit2016marscientistc
+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
nielit2016marscientistc
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
nielit2016marscientistc
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
nielit2016marscientistc
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
nielit2016marscientistc
0
votes
0
answers
26
NIELIT 2016 MAR Scientist C  Section B: 14
Find the area bounded by the curve $y=\sqrt{5x^{2}}$ and $y=\mid x1 \mid$ $\dfrac{2}{0}(2\sqrt{6}\sqrt{3})\dfrac{5}{2}$ $\dfrac{2}{3}(6\sqrt{6}+3\sqrt{3})+\dfrac{5}{2}$ $2(\sqrt{6}\sqrt{3})5$ $\dfrac{2}{3}(\sqrt{6}\sqrt{3})+5$
asked
Apr 2
in
Mathematical Logic
by
Lakshman Patel RJIT

14
views
nielit2016marscientistc
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 $7x8y+3z+25=0$ $7x+8y+3z+25=0$ $7x8y+3z25=0$ $7x8y3z25=0$
asked
Apr 2
in
Mathematical Logic
by
Lakshman Patel RJIT

12
views
nielit2016marscientistc
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
nielit2016marscientistc
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
nielit2016marscientistc
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
nielit2016marscientistc
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
nielit2016marscientistc
0
votes
1
answer
32
UGCNETDec2006II: 2
The proposition ~ q ∨ p is equivalent to :
answered
Apr 2
in
Mathematical Logic
by
immanujs

45
views
ugcnetdec2006ii
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
nielit2017decscientistb
0
votes
2
answers
34
UGCNETJan2017II: 2
Match the following : ...
asked
Mar 24
in
Mathematical Logic
by
jothee

75
views
ugcnetjan2017ii
mathematicallogic
0
votes
1
answer
35
UGCNETJan2017II: 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
ugcnetjan2017ii
discretemathematics
propositionallogic
+5
votes
3
answers
36
GATE2020CS45
For $n>2$, let $a \in \{0,1\}^n$ be a nonzero 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
gate2020cs
numericalanswers
+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
madeeasytestseries
firstorderlogic
mathematicallogic
+7
votes
4
answers
38
GATE2020CS1
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
gate2020cs
engineeringmathematics
+35
votes
8
answers
39
GATE20021.8
"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
gate2002
mathematicallogic
normal
propositionallogic
+32
votes
5
answers
40
GATE20002.7
Let $a, b, c, d$ be propositions. Assume that the equivalence $a ⇔ ( b \vee \neg b)$ and $b ⇔c$ hold. Then the truthvalue of the formula $(a ∧ b) → (a ∧ c) ∨ d$ is always True False Same as the truthvalue of $b$ Same as the truthvalue of $d$
answered
Feb 26
in
Mathematical Logic
by
Pratyush Priyam Kuan

3.1k
views
gate2000
mathematicallogic
normal
propositionallogic
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