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Propositional and first order logic.
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zeal test descrete
My doubt is in second hasse diagram for (I,g) lub should be I and j so it is not lattice please correct me if i amwrong
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GATEBOOK2019DM118
Everyone has exactly one best friend Which of the following first order logic statements correctly represents above English statement? $BF(x,y)$ means $x$ and $y$ are best friends $S1 : \forall x \exists y \forall z (BF(x,y) \wedge \sim BF(x,z) \rightarrow (y \neq z ... \forall z [(y \neq z)] \rightarrow \sim BF(x,z))$ Only $S1$ Only $S2$ Both $S1$ and $S2$ None of the two
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GATEBOOK2019DM112
Translate the following logic statement to English where, $A(x)$: $x$ is African, $F(x,y)$: x and y are friends. The universe for $x$ and $y$ is all the people in the world. $$\forall x \exists y((A(x) \vee (F(x,y)))$$ Every African has some African friend Every person who is not African has at least one friend Every person who has friend is not African None of these
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GATEBOOK2019DM114
Consider the following inference system: $P$ $\neg P \vee Q$ $\neg Q \vee R$ Which of the following is a valid conclusion ? $R$ $ \neg R$ $ \neg Q$ $ \neg R \wedge Q$
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GATEBOOK2019DM115
Let $I$ denote the formula $ (q \rightarrow p) \rightarrow (p \rightarrow q)$ and $II$ denote the formula $(p\rightarrow q) \wedge q$ Which of the following is true? $I$ is not tautology and $II$ is not satisfiable $I$ is not tautology and $II$ is satisfiable $I$ is satisfiable and $II$ is not satisfiable $I$ is tautology and $II$ is satisfiable
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GATEBOOK2019DM116
Which of the following statements is not necessarily true ? $\forall x \forall y P(x,y) \Leftrightarrow \forall y \forall x P(x,y)$ $ \exists x \exists y P(x,y) \Leftrightarrow \exists y \exists x P(x,y)$ $\forall x \exists y P(x,y) \Rightarrow \exists y \forall x P(x,y) $ $ \exists y \forall x P(x,y) \Rightarrow \forall x \exists y P(x,y)$
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GATEBOOK2019DM119
Which of the following statements is FALSE $\exists x (P(x) \rightarrow Q(x)) \equiv \forall x P(x) \rightarrow \exists x Q(x) $ $\exists x (P(x) \vee Q(x)) \equiv \exists x P(x) \vee \exists x Q(x) $ $\forall x (P(x)\wedge Q(x)) \equiv \forall x P(x) \wedge \forall x Q(x) $ $\exists x (P(x)\wedge Q(x)) \equiv \exists x P(x) \wedge \exists x Q(x) $
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gb2019dm1
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Well ordered Set
I understood the Concept of well ordered Set.But i am little bit confused in finding the least element.Can please anybody clarify the concept of finding the least element in a Poset with an example.
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settheory&algebra
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9
Self Doubt on order of execution of statements in Propositional Logic for implication operator
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Propositional and First Order Logic GATECS2006
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Discrete mathematics
every sublattice of a distributive lattice is also a distributive lattice? explain above line if possible then take an example..!
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kennethrosen
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Matrix Eigen Value
A 3× 3 real matrix has an eigen value i, then its other two eigen values can be (A) 0, 1. (B) 1, i. (C) 2i, 2i. (D) 0, i.
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engineeringmathematics
linearalgebra
matrix
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1
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13
Graph theory
Stmt 1: A simple graph is necessarily connected if E > (n1)*(n2)/2. Stmt2: A simple graph with n vertices and k components has at least nk edges. Can you please explain how are these results derived?
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graphtheory
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#virtual gate
Four siblings go shopping with their father. If Abhay gets shoes, then Asha does not get a necklace. If Arun gets a Tshirt, then Aditi gets bangles. If Abhay does not get shoes or Aditi gets bangles, the mother will be happy. Which of the following is true? (a) If ... If the mother is not happy, then Asha did not get a necklace and Arun did not get a Tshirt. (d) None of the above.
[closed]
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15
Lattice
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lattice
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16
Made easy test series
What is the difference between (ii) and (iv). I understood (ii) as "All the engineers like at least some doctor" What will be the translation for (iv) ?
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17
Thegatebook
Which of the following propositional logic formulae is TRUE when exactly two of $p,q $ and $r$ are TRUE? $(A)$ $((p↔q)∧r)∨(p∧q∧¬r))$ $(B)$ $(¬(p↔q)∧r)∨(p∧q∧¬r))$ $(C)$ $((p↔q)∧r)∨(p∧q∧¬r))$ $(D)$ $(¬(p↔q)∧r)∧(p∧q∧¬r))$
[closed]
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propositionallogic
+14
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4
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18
GATE20011.3
Consider two wellformed formulas in propositional logic $F_1: P \Rightarrow \neg P$ $F_2: (P \Rightarrow \neg P) \lor ( \neg P \Rightarrow P)$ Which one of the following statements is correct? $F_1$ is satisfiable, $F_2$ is valid $F_1$ unsatisfiable, $F_2$ is satisfiable $F_1$ is unsatisfiable, $F_2$ is valid $F_1$ and $F_2$ are both satisfiable
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gate2001
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easy
propositionallogic
0
votes
1
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19
why is the conclusion incorrect for the below premises ?
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Mk Utkarsh
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mathematicallogic
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votes
1
answer
20
universe of discourse[ propositional logic]
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Shubham Aggarwal
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13
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0
votes
1
answer
21
gatezeal testseries
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zeal
testseries
+37
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4
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22
GATE200423, ISRO200732
Identify the correct translation into logical notation of the following assertion. Some boys in the class are taller than all the girls Note: $\text{taller} (x, y)$ is true if $x$ is taller than $y$. $(\exists x) (\text{boy}(x) \rightarrow (\forall y) (\text{girl}(y) \ ... )))$ $(\exists x) (\text{boy}(x) \land (\forall y) (\text{girl}(y) \rightarrow \text{taller}(x, y)))$
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gate2004
mathematicallogic
easy
isro2007
firstorderlogic
+26
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6
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23
GATE2008IT21
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 $\beta$ is a first order formula with no free variable. $[\beta \rightarrow (\exists x, \alpha(x))] \rightarrow [\forall x, ... ) \rightarrow \beta]$ $[(\forall x, \alpha(x)) \rightarrow \beta] \rightarrow [\forall x, \alpha(x) \rightarrow \beta]$
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gate2008it
firstorderlogic
normal
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0
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24
self doubt
translate english statements into predicate. Q)No one in your school owns both a bicycle and a motorcycle. i got this $\neg(\forall x(S(x)\implies (B(x)\wedge M(x)))$
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3
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25
GATE200332
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) $((∀x)[α] ⇒ (∀x)[β]) ⇒ (∀x)[α ⇒ β]$ $(∀x)[α] ⇒ (∃x)[α ∧ β]$ $((∀x)[α ∨ β] ⇒ (∃x)[α]) ⇒ (∀x)[α]$ $(∀x)[α ⇒ β] ⇒ (((∀x)[α]) ⇒ (∀x)[β])$
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firstorderlogic
normal
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0
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26
#books
Some cat are intelligent express into first order logic if domain are animals
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#first
firstorderlogic
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27
#notesbook
you cannot ride the roller coaster if you are under 4 feet tall unless you are old then 16 years convert into propostional logic
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1
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28
matrix multiplication
consider 3 matrices A[100*200] B[200*50]] C[50*30] Suppose a computer takes 1) 1 microsecond to multiply 2 numbers. 2) almost 0 second to perform Addition. Then find out how much time the computer will take to Multiply matrices in All possible ways. Assume the ... to be continuous without any time delay. options are 1) 0.5 seconds 2) 1.5 seconds 3) 2 seconds 4) 3 seconds
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29
gate zeal test series
is there any shortcut to do this question fast ?
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30
gate zeal test series
i didn't read the concept related to strongly connected components please it describe it for this question
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31
gate zeal test series
Its answer is D) can anyone explain what is difference between a) and d)
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32
gate zeal test series
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GATEBOOK2019DM110
Assuming a nonempty universe, the formula $(\forall x P(x) \vee \exists y P(y))$ is equivalent to $\exists x (P(x))$ $ (\forall x P(x))$ $ \neg (\forall x P(x))$ $ \neg (\exists x (P(x))$
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GATEBOOK2019DM17
Which of the following propositional formulae is a tautology? $(\neg p \vee r ) \rightarrow (p \vee \neg r)$ $ \neg ( p \rightarrow (p \wedge q ))$ $ r \rightarrow ( p \wedge \neg r )$ $ ( p \leftrightarrow q ) \vee (p \leftrightarrow \neg q)$
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35
Virtual gate
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36
Gate zeal booklet
1)How to approach question no. 34,36
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Gate zeal booklet
How to write the last line of Qno. 19  irrespective of whether the system has been armed the alarm should go off when there is fire For Qno 20 I am getting iii) and iv) as true but answer is a) please check the 5th one
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GateZeal booklet
answer for this is A) My doubt is why D) can't be the answer
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Descrete math zeal booklet
Its answer is a) but here more(x,y) is given means it should be like this  x is more than y then isn't a) is wrong
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40
Gate zeal booklet
Answer for this is a) but m getting d) as right option please check it
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