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3
answers
1
GATE 2008 | Question 21
I have been trying to solve the question GATE CSE 2008 Question. Are the following two representations logically equivalent ? $\beta \rightarrow (\exists x, \alpha (x))$ $\exists x, \beta \rightarrow \alpha (x)$
commented
in
Mathematical Logic
Feb 17, 2023
991
views
gatecse-2008
mathematical-logic
first-order-logic
normal
12
answers
2
GATE CSE 2016 Set 1 | Question: 19
Consider the following code segment. x = u - t; y = x * v; x = y + w; y = t - z; y = x * y; The minimum number of total variables required to convert the above code segment to static single assignment form is __________.
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in
Compiler Design
Jan 28, 2023
27.5k
views
gatecse-2016-set1
compiler-design
static-single-assignment
normal
numerical-answers
6
answers
3
GATE CSE 2013 | Question: 65
The current erection cost of a structure is Rs. $13,200.$ If the labour wages per day increase by $1/5$ of the current wages and the working hours decrease by $1/24$ of the current period, then the new cost of erection in Rs. is $16,500$ $15,180$ $11,000$ $10,120$
answered
in
Quantitative Aptitude
Jan 24, 2023
8.1k
views
gatecse-2013
quantitative-aptitude
normal
work-time
2
answers
4
Programming and ds
How many number of add and remove operations are required to access 26th element of a queue of 50 elements,so that the original queue remains the same after the access is Note:-Direct accessing through the index is not included.
answered
in
Programming in C
Jan 23, 2023
407
views
programming-in-c
13
answers
5
GATE CSE 2017 Set 2 | Question: 55
Consider the following C program. #include<stdio.h> #include<string.h> int main() { char* c="GATECSIT2017"; char* p=c; printf("%d", (int)strlen(c+2[p]-6[p]-1)); return 0; } The output of the program is _______
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in
Programming in C
Jan 15, 2023
27.6k
views
gatecse-2017-set2
programming-in-c
numerical-answers
array
pointers
8
answers
6
GATE IT 2007 | Question: 45
The line $T$ in the following figure is permanently connected to the ground. Which of the following inputs $(X_1 X_2 X_3 X_4)$ will detect the fault ? $0000$ $0111$ $1111$ None of these
answered
in
Digital Logic
Nov 11, 2022
12.2k
views
gateit-2007
digital-logic
circuit-output
normal
1
answer
7
ISI2021-PCB-C10
Suppose instead of a decoder with n input bits (n is even) to access a memory of size 2^n, one uses two decoders of input sizes k bits and (n-k) bits. Explain how these two decoders can be used to access the memory of size 2^N. ... address decoding time. Justify your answer. Assume that the time complexity of the decoder is measured by the number of output lines of that decoder.
answered
in
Digital Logic
Nov 8, 2022
567
views
digital-logic
decoder
isi
1
answer
8
Self-doubt
How many NOR Gates required to realize the given logical expression? Y = (A+C)(A+D')(A+B+C')
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in
Digital Logic
Nov 8, 2022
455
views
1
answer
9
ISI2020-PCB-CS: 10
Suppose instead of a decoder with $n$ input bits ( $n$ is even) to access a memory of size $2^{n}$, one uses two decoders of input sizes $k$ bits and $(n-k)$ bits. Explain how these two decoders can be used to access the ... address decoding time. Justify your answer. Assume that the time complexity of the decoder is measured by the number of output lines of that decoder.
answered
in
Digital Logic
Nov 7, 2022
381
views
isi2020-pcb-cs
digital-logic
combinational-circuit
decoder
descriptive
3
answers
10
Applied test series question
A 4-bit carry lookahead adder adds two 4-bit numbers. The adder is designed without making use of the EX-OR gates. The propagation delay for all gates is given as 2.4 time units. What will be the overall delay of adder if we assume that inputs ... AND, Or gates. can someone explain me this in a deatiled manner as i am not able to find the appropriate solution for it ?
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in
Digital Logic
Nov 7, 2022
620
views
test-series
digital-logic
adder
1
answer
11
How many m-input NAND gates will be required to construct a n-input NAND gate, where (m <= n)?
How many $m-$ input NAND gates are needed to construct a $n-$ input NAND gate, where $m \leq n$ Examples: > constructing $3-$input NAND gate using $2-$ ... solution to this problem, or is there NO general solution available (i.e., a localized solution may exist)?
asked
in
Digital Logic
Nov 7, 2022
335
views
digital-logic
min-no-gates
self-doubt
4
answers
12
GATE CSE 2005 | Question: 41
What is the first order predicate calculus statement equivalent to the following? "Every teacher is liked by some student" $∀(x)\left[\text{teacher}\left(x\right) → ∃(y) \left[\text{student}\left(y\right) → \text{likes}\left(y,x\right)\right]\right]$ ...
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in
Mathematical Logic
Nov 7, 2022
11.7k
views
gatecse-2005
mathematical-logic
easy
first-order-logic
10
answers
13
GATE CSE 2002 | Question: 1.8
"If $X$ then $Y$ unless $Z$" is represented by which of the following formulas in propositional logic? ("$\neg$" is negation, "$\land$" is conjunction, and "$\rightarrow$" is implication) $(X\land \neg Z) \rightarrow Y$ $(X \land Y) \rightarrow \neg Z$ $X \rightarrow(Y\land \neg Z)$ $(X \rightarrow Y)\land \neg Z$
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in
Mathematical Logic
Nov 7, 2022
14.7k
views
gatecse-2002
mathematical-logic
normal
propositional-logic
10
answers
14
GATE CSE 2017 Set 1 | Question: 29
Let $p$, $q$ and $r$ be propositions and the expression $\left ( p\rightarrow q \right )\rightarrow r$ be a contradiction. Then, the expression $\left ( r\rightarrow p \right )\rightarrow q$ is a tautology a contradiction always TRUE when $p$ is FALSE always TRUE when $q$ is TRUE
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in
Mathematical Logic
Nov 7, 2022
10.5k
views
gatecse-2017-set1
mathematical-logic
propositional-logic
8
answers
15
GATE CSE 2021 Set 1 | Question: 7
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 ... but $S_2$ is not a tautology $S_1$ is not a tautology but $S_2$ is a tautology Neither $S_1$ nor $S_2$ is a tautology
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in
Mathematical Logic
Nov 7, 2022
8.1k
views
gatecse-2021-set1
mathematical-logic
propositional-logic
1-mark
7
answers
16
GATE CSE 2000 | Question: 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 $d$
commented
in
Mathematical Logic
Nov 7, 2022
12.1k
views
gatecse-2000
mathematical-logic
normal
propositional-logic
7
answers
17
GATE CSE 2003 | Question: 32
Which of the following is a valid first order formula? (Here \(\alpha\) and \(\beta\) are first order formulae with $x$ as their only free variable) $((∀x)[α] ⇒ (∀x)[β]) ⇒ (∀x)[α ⇒ β]$ $(∀x)[α] ⇒ (∃x)[α ∧ β]$ $((∀x)[α ∨ β] ⇒ (∃x)[α]) ⇒ (∀x)[α]$ $(∀x)[α ⇒ β] ⇒ (((∀x)[α]) ⇒ (∀x)[β])$
commented
in
Mathematical Logic
Nov 7, 2022
16.8k
views
gatecse-2003
mathematical-logic
first-order-logic
normal
11
answers
18
GATE CSE 2016 Set 2 | Question: 01
Consider the following expressions: $false$ $Q$ $true$ $P\vee Q$ $\neg Q\vee P$ The number of expressions given above that are logically implied by $P \wedge (P \Rightarrow Q)$ is ___________.
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in
Mathematical Logic
Nov 7, 2022
19.8k
views
gatecse-2016-set2
mathematical-logic
normal
numerical-answers
propositional-logic
9
answers
19
GATE IT 2005 | Question: 36
Let $P(x)$ and $Q(x)$ ...
answered
in
Mathematical Logic
Nov 6, 2022
14.8k
views
gateit-2005
mathematical-logic
first-order-logic
normal
6
answers
20
GATE CSE 2003 | Question: 72
The following resolution rule is used in logic programming. Derive clause $(P \vee Q)$ from clauses $(P\vee R),(Q \vee ¬R)$ Which of the following statements related to this rule is FALSE? $((P ∨ R)∧(Q ∨ ¬R))⇒(P ∨ Q)$ ... if $(P ∨ R)∧(Q ∨ ¬R)$ is satisfiable $(P ∨ Q)⇒ \text{FALSE}$ if and only if both $P$ and $Q$ are unsatisfiable
commented
in
Mathematical Logic
Nov 6, 2022
14.1k
views
gatecse-2003
mathematical-logic
normal
propositional-logic
8
answers
21
GATE CSE 2020 | Question: 39
Which one of the following predicate formulae is NOT logically valid? Note that $W$ is a predicate formula without any free occurrence of $x$. $\forall x (p(x) \vee W) \equiv \forall x \: ( px) \vee W$ ... $\exists x(p(x) \rightarrow W) \equiv \forall x \: p(x) \rightarrow W$
commented
in
Mathematical Logic
Nov 6, 2022
17.1k
views
gatecse-2020
first-order-logic
mathematical-logic
2-marks
6
answers
22
GATE CSE 1992 | Question: 92,xv
Which of the following predicate calculus statements is/are valid? $(\forall (x)) P(x) \vee (\forall(x))Q(x) \implies (\forall (x)) (P(x) \vee Q(x))$ $(\exists (x)) P(x) \wedge (\exists (x))Q(x) \implies (\exists (x)) (P(x) \wedge Q(x))$ ... $(\exists (x)) (P(x) \vee Q(x)) \implies \sim (\forall (x)) P(x) \vee (\exists (x)) Q(x)$
commented
in
Mathematical Logic
Nov 6, 2022
16.4k
views
gate1992
mathematical-logic
normal
first-order-logic
5
answers
23
GATE CSE 2015 Set 2 | Question: 55
Which one of the following well-formed formulae is a tautology? $\forall x \, \exists y \, R(x,y) \, \leftrightarrow \, \exists y \, \forall x \, R(x, y)$ ... $\forall x \, \forall y \, P(x,y) \, \rightarrow \, \forall x \, \forall y \, P(y, x)$
comment edited
in
Mathematical Logic
Nov 6, 2022
21.0k
views
gatecse-2015-set2
mathematical-logic
normal
first-order-logic
6
answers
24
GATE CSE 2003 | Question: 33
Consider the following formula and its two interpretations \(I_1\) and \(I_2\). \(\alpha: (\forall x)\left[P_x \Leftrightarrow (\forall y)\left[Q_{xy} \Leftrightarrow \neg Q_{yy} \right]\right] \Rightarrow (\forall x)\left[\neg P_x\right]\) \(I_1\) : Domain: ... I_1\) does not Neither \(I_1\) nor \(I_2\) satisfies \(\alpha\) Both \(I_1\) and \(I_2\) satisfies \(\alpha\)
commented
in
Mathematical Logic
Nov 6, 2022
15.8k
views
gatecse-2003
mathematical-logic
difficult
first-order-logic
3
answers
25
Predicate Translation
S(x): x is a Student P(x): x is a Professor A(x, y): x has asked a question to y Domain not given, so we have to think about default domain Q1) Translate There is a student who has asked every professor a question Q2) Translate ... a professor who has been asked a question by every student Q4) Translate There is a student who has been asked a question by every professor
answered
in
Mathematical Logic
Nov 6, 2022
672
views
propositional-logic
mathematical-logic
discrete-mathematics
2
answers
26
is this argument valid: {P->Q , Q->R}-> R'
commented
in
Mathematical Logic
Nov 6, 2022
1.2k
views
mathematical-logic
1
answer
27
Translate the given statement into propositional logicexpressions:“A man qualifies for the marathon if his best previous time is less than 3 hours and a woman qualifies for the marathon if her best previous time is less than 3.5 hours.
answered
in
Mathematical Logic
Nov 6, 2022
694
views
discrete-mathematics
mathematical-logic
propositional-logic
2
answers
28
Let 𝐼(𝑥)be the statement “𝑥has an Internet connection” and 𝐶(𝑥,𝑦)be the statement “𝑥and𝑦have chatted over the Internet,” where the domain for the variables 𝑥and 𝑦consists of all students in your class. Use quantifiers to express the followingstatement:“Everyone in your class with an Internet connection has chatted over the Internet with at least one other student in your class.
answered
in
Mathematical Logic
Nov 6, 2022
697
views
discrete-mathematics
first-order-logic
9
answers
29
GATE IT 2008 | Question: 21
Which of the following first order formulae is logically valid? Here $\alpha(x)$ is a first order formula with $x$ as a free variable, and $\beta$ ... $[(\forall x, \alpha(x)) \rightarrow \beta] \rightarrow [\forall x, \alpha(x) \rightarrow \beta]$
answered
in
Mathematical Logic
Nov 5, 2022
15.1k
views
gateit-2008
first-order-logic
normal
7
answers
30
GATE CSE 2018 | Question: 51
A processor has $16$ integer registers $\text{(R0, R1}, \ldots ,\text{ R15)}$ and $64$ floating point registers $\text{(F0, F1}, \ldots , \text{F63)}.$ It uses a $2\text{- byte}$ instruction format. There are four categories of ... $\text{(1F)}.$ The maximum value of $\text{N}$ is _________.
answered
in
CO and Architecture
Nov 4, 2022
24.2k
views
gatecse-2018
co-and-architecture
machine-instruction
instruction-format
numerical-answers
2-marks
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