Recent questions tagged mathematical-logic

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1

why is the conclusion incorrect for the below premises ?

asked 4 days ago in Mathematical Logic by radha gogia Loyal (7.7k points) | 72 views

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2

GATEBOOK-2019-DM1-1
Which of the following first order logic statement is equivalent to below statement? If anyone cheats, everyone suffers. $S_1 \forall x (\text{cheat}(x) \to \forall y \text{ suffer}(y))$ $S_2: \forall x\forall y (\text{cheat}(x) \to \text{ suffer}(y))$ Only S1 Only S2 Both S1 and S2 None

asked Oct 28 in Mathematical Logic by GATEBOOK Active (1.8k points) | 54 views

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3

GATEBOOK-2019-DM1-2
Which of the following first order logic statements is VALID? $\neg\forall x \{ P(x) \vee ∃y [Q(y) \wedge P(y)] \} ≡ ∃x \{ \neg P(x) \wedge \forall y [(P(y) → \neg Q(y)) \vee (Q(y) → \neg P(y))] \}$ $\neg\forall x \{ P(x) \vee ∃y [Q(y) \wedge P(y)] \} ≡ ∃x \{ \neg ... ∃y [Q(y) \wedge P(y)] \} ≡ ∃x \{ \neg P(x) \wedge \forall y [\neg(P(y) → \neg Q(y)) \vee (Q(y) → \neg P(y))] \}$

asked Oct 28 in Mathematical Logic by GATEBOOK Active (1.8k points) | 24 views

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GATEBOOK-2019-DM1-3
Which of the following formulae is a formalization of the sentence: "There is a $\text{Computer}$ which is not used by any $\text{Student}$" $ \exists x (\text{Computer}(x) \wedge \forall y. (\sim \text{Student}(y) \wedge \sim \text{Uses}(y,x))) $ $ \ ... $ \exists x (\text{Computer} (x) \rightarrow \forall y . (\sim \text{Student} (y) \wedge \sim \text{Uses}(y,x)))$

asked Oct 28 in Mathematical Logic by GATEBOOK Active (1.8k points) | 13 views

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5

GATEBOOK-2019-DM1-4
Minesweeper is a single-player computer game invented by Robert Donner in 1989. A unary predicate mine is defined, where $\text{mine}(x)$ means that the cell $x$ contains a mine $$\exists x_1, \dots , \exists x_n \left(\bigwedge_{i=1}^{n} \text{mine}(x_i) ... $n$ mines in the game There are at least $n$ mines in the game There are at most $n$ mines in the game None of the above

asked Oct 28 in Mathematical Logic by GATEBOOK Active (1.8k points) | 14 views

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6

GATEBOOK-2019-DM1-5
Which of the below first order logic formulae represent the sentence There is a student who is loved by every other student Here, $\text{Loves}(x,y)$ means $x$ loves $y$ $\exists x (\text{Student} (x) \wedge \forall y (\text{Student} (y) \wedge \neg (x=y) \rightarrow ... \text{Student} (x) \wedge \forall y (\text{Student} (y) \wedge \neg (x=y) \rightarrow \text{Loves} (y,x))) $

asked Oct 28 in Mathematical Logic by GATEBOOK Active (1.8k points) | 15 views

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GATEBOOK-2019-DM1-6
Which of the following propositional formulae represents the sentence, 'He will come in the 8:15 or the 9:15 train; if the former, he will have time to visit us', where $p$ means 'He will come on the 8:15' $q$ means 'He will come on the 9:15' $r$ means 'He will have time ... vee q \rightarrow r $ $ ( p \rightarrow q) \wedge ( p \vee r )$ $ (p \vee q ) \wedge (p \rightarrow r)$

asked Oct 28 in Mathematical Logic by GATEBOOK Active (1.8k points) | 14 views

+1 vote

1 answer

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GATEBOOK-2019-DM1-7
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)$

asked Oct 28 in Mathematical Logic by GATEBOOK Active (1.8k points) | 30 views

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GATEBOOK-2019-DM1-8
Which of the following inference system is valid? $ (p \vee q ) \rightarrow r, r \models \neg p $ $ p, \neg p \leftrightarrow q \models \neg q$ $ (p \wedge q) \rightarrow r, \neg r \models p \vee q$ $ p \wedge q \models p \leftrightarrow \neg q$

asked Oct 28 in Mathematical Logic by GATEBOOK Active (1.8k points) | 12 views

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10

GATEBOOK-2019-DM1-9
Which of the following formulas represents the sentence, 'Share prices will go up, and if interest rates go up too, there will be a recession', where ; $p$ means 'share prices will go up' $q$ means 'interest rates will go up' $r$ means 'there will be a recession'. $ p \wedge q \rightarrow r$ $ p \wedge (q \rightarrow r)$ $ p \rightarrow q \wedge r$ $ (p \rightarrow q) \vee r$

asked Oct 28 in Mathematical Logic by GATEBOOK Active (1.8k points) | 10 views

+1 vote

1 answer

11

GATEBOOK-2019-DM1-10
Assuming a non-empty 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))$

asked Oct 28 in Mathematical Logic by GATEBOOK Active (1.8k points) | 45 views

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12

GATEBOOK-2019-DM1-11
Suppose that $P(x,y)$ means "x is a parent of y" and $M(x)$ means "x is a male". If $F(v,w)$ equals $M(v) \wedge \exists x \exists y (P(x,y) \wedge P(x,v) \wedge (y \neq v ) \wedge P(y,w)), $ the meaning of the expression $F(v,w)$ is $v$ is a brother of $w$ $v$ is an uncle of $w$ $v$ is a grandfather of $w$ $v$ is a nephew of $w$

asked Oct 28 in Mathematical Logic by GATEBOOK Active (1.8k points) | 16 views

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GATEBOOK-2019-DM1-12
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

asked Oct 28 in Mathematical Logic by GATEBOOK Active (1.8k points) | 57 views

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14

GATEBOOK-2019-DM1-13
Consider the following statement $ \exists x \exists y (\text{PARENT}(x, \text{Ramu}) \wedge \text{PARENT}(y, \text{Ramu}))$ where $\text{PARENT}(x,y)$ means $x$ is a parent of $y.$ Which of the following statement is true about above first order logic statement ? Ramu has at least one parent Ramu has at least two parents Ramu has at most one parent Ramu has at most two parents

asked Oct 28 in Mathematical Logic by GATEBOOK Active (1.8k points) | 9 views

+1 vote

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GATEBOOK-2019-DM1-14
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$

asked Oct 28 in Mathematical Logic by GATEBOOK Active (1.8k points) | 21 views

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16

GATEBOOK-2019-DM1-15
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

asked Oct 28 in Mathematical Logic by GATEBOOK Active (1.8k points) | 15 views

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17

GATEBOOK-2019-DM1-16
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)$

asked Oct 28 in Mathematical Logic by GATEBOOK Active (1.8k points) | 12 views

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18

GATEBOOK-2019-DM1-17
Every true Indian thinks about politics and Jayaprakash Narayana thinks about politics Which of the following is valid conclusion? A. Jayaprakash Narayana is true Indian B. Jayaprakash Narayana is politician C. Jayaprakash Narayana is not true Indian D. None of the above

asked Oct 28 in Mathematical Logic by GATEBOOK Active (1.8k points) | 7 views

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19

GATEBOOK-2019-DM1-18
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

asked Oct 28 in Mathematical Logic by GATEBOOK Active (1.8k points) | 13 views

+1 vote

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20

GATEBOOK-2019-DM1-19
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) $

asked Oct 28 in Mathematical Logic by GATEBOOK Active (1.8k points) | 10 views

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21

GATEBOOK-2019-DM1-20
A binary operator is defined as follows $P \Updownarrow Q = \sim P \wedge Q$ Which of the following statement is equivalent to $P \rightarrow Q $ $\sim P \Updownarrow Q$ $\sim( P \Updownarrow Q)$ $\sim( \sim P \Updownarrow Q)$ $\sim ( \sim P \Updownarrow \sim Q)$

asked Oct 28 in Mathematical Logic by GATEBOOK Active (1.8k points) | 14 views

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22

Quantifiers
Given that B(x) means "x is a bear" F(x) means "x is a fish" and E(x,y) means "x eats y" What is the best English translation of $\forall x [F(x)\rightarrow \forall y(E(y,x)\rightarrow B(y))]$ A) All fish eat bears B) Every bears can eat fish C) Only bears eat fish D) Bears eat only fish

asked Oct 2 in Mathematical Logic by Lakshman Patel RJIT Boss (14.4k points) | 42 views

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23

Nested Quantifiers
If we have ∀x(p(x)) then in boolean algebra form we can write this statement as (P1 + P2) where + signifies OR which makes it very easy to deal with. So likewise is there any way to have a view of a statement like ∀x∀y(R(x,y)) into boolean form?

asked Sep 29 in Mathematical Logic by sushil1997 (35 points) | 20 views

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24

No idea about what to study in FIRST ORDER LOGIC

asked Sep 28 in Mathematical Logic by iarnav Loyal (9k points) | 43 views

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25

PREDICATE LOGIC DOUBT
Only Area 51 has Extra-Terresstrials A(x) = x is Area 51 E(x) = x has Extra-Terresstrials Which of the following is correct? (∀x)(A(x) -> E(x)) (∀x)(E(x) -> A(x)) (∀x)(A(x) <-> E(x))

asked Sep 27 in Mathematical Logic by Balaji Jegan Active (3.1k points) | 36 views

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26

Propositional Logic
Are the following first order logic formulae equivalent?

asked Sep 25 in Mathematical Logic by srestha Veteran (101k points) | 53 views

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27

Mathematical Logic
prove $(¬A→¬B)∧(A→C)→(B→C)$

asked Sep 20 in Mathematical Logic by Vishnathan (285 points) | 28 views

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28

Predicate logic gatebook test on logic Q18

asked Sep 8 in Mathematical Logic by Sandy Sharma Junior (975 points) | 59 views

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29

Predicate logic gatebook test on logic Q13

asked Sep 8 in Mathematical Logic by Sandy Sharma Junior (975 points) | 25 views

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30

Predicate logic gatebook test on logic Q4

asked Sep 8 in Mathematical Logic by Sandy Sharma Junior (975 points) | 28 views

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