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Recent questions tagged gb2019dm1
+2
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1
GATEBOOK2019DM11
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, 2018
in
Mathematical Logic
by
GATEBOOK
Boss
(
11.4k
points)

254
views
gb2019dm1
firstorderlogic
discretemathematics
mathematicallogic
quantifiers
0
votes
1
answer
2
GATEBOOK2019DM12
Which of the following first order logic statements is VALID? $\neg\forall x \{ P(x) \vee ∃y [Q(y) \wedge P(y)] \} ≡ ∃x \{ \neg P(x) \wedge \forall y [(P(y) → \neg Q(y)) \vee (Q(y) → \neg P(y))] \}$ ...
asked
Oct 28, 2018
in
Mathematical Logic
by
GATEBOOK
Boss
(
11.4k
points)

129
views
gb2019dm1
discretemathematics
mathematicallogic
firstorderlogic
0
votes
1
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3
GATEBOOK2019DM13
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, 2018
in
Mathematical Logic
by
GATEBOOK
Boss
(
11.4k
points)

98
views
gb2019dm1
discretemathematics
mathematicallogic
quantifiers
0
votes
1
answer
4
GATEBOOK2019DM14
Minesweeper is a singleplayer computer game invented by Robert Donner in 1989. A unary predicate mine is defined, where $\text{mine}(x)$ means that the cell $x$ ... $n$ mines in the game There are at most $n$ mines in the game None of the above
asked
Oct 28, 2018
in
Mathematical Logic
by
GATEBOOK
Boss
(
11.4k
points)

213
views
gb2019dm1
discretemathematics
mathematicallogic
quantifiers
0
votes
0
answers
5
GATEBOOK2019DM15
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 $y$ ...
asked
Oct 28, 2018
in
Mathematical Logic
by
GATEBOOK
Boss
(
11.4k
points)

106
views
gb2019dm1
discretemathematics
mathematicallogic
quantifiers
0
votes
0
answers
6
GATEBOOK2019DM16
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 in the $8:15$ train' $q$ means 'He will come in the $9:15$ train' $r$ ... $ ( p \rightarrow q) \wedge ( p \vee r )$ $ (p \vee q ) \wedge (p \rightarrow r)$
asked
Oct 28, 2018
in
Mathematical Logic
by
GATEBOOK
Boss
(
11.4k
points)

111
views
gb2019dm1
discretemathematics
mathematicallogic
propositionallogic
+2
votes
1
answer
7
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)$
asked
Oct 28, 2018
in
Mathematical Logic
by
GATEBOOK
Boss
(
11.4k
points)

73
views
gb2019dm1
discretemathematics
propositionallogic
mathematicallogic
0
votes
1
answer
8
GATEBOOK2019DM18
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, 2018
in
Mathematical Logic
by
GATEBOOK
Boss
(
11.4k
points)

78
views
gb2019dm1
discretemathematics
mathematicallogic
+1
vote
0
answers
9
GATEBOOK2019DM19
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, 2018
in
Mathematical Logic
by
GATEBOOK
Boss
(
11.4k
points)

128
views
gb2019dm1
discretemathematics
mathematicallogic
propositionallogic
+2
votes
1
answer
10
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))$
asked
Oct 28, 2018
in
Mathematical Logic
by
GATEBOOK
Boss
(
11.4k
points)

142
views
gb2019dm1
discretemathematics
propositionallogic
mathematicallogic
0
votes
0
answers
11
GATEBOOK2019DM111
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, 2018
in
Mathematical Logic
by
GATEBOOK
Boss
(
11.4k
points)

65
views
gb2019dm1
discretemathematics
mathematicallogic
propositionallogic
quantifiers
0
votes
2
answers
12
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
asked
Oct 28, 2018
in
Mathematical Logic
by
GATEBOOK
Boss
(
11.4k
points)

155
views
gb2019dm1
discretemathematics
mathematicallogic
propositionallogic
quantifiers
+1
vote
2
answers
13
GATEBOOK2019DM113
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 ... 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, 2018
in
Mathematical Logic
by
GATEBOOK
Boss
(
11.4k
points)

154
views
gb2019dm1
discretemathematics
mathematicallogic
firstorderlogic
quantifiers
+1
vote
0
answers
14
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$
asked
Oct 28, 2018
in
Mathematical Logic
by
GATEBOOK
Boss
(
11.4k
points)

68
views
gb2019dm1
discretemathematics
mathematicallogic
propositionallogic
+2
votes
1
answer
15
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
asked
Oct 28, 2018
in
Mathematical Logic
by
GATEBOOK
Boss
(
11.4k
points)

103
views
gb2019dm1
discretemathematics
mathematicallogic
propositionallogic
+1
vote
0
answers
16
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)$
asked
Oct 28, 2018
in
Mathematical Logic
by
GATEBOOK
Boss
(
11.4k
points)

82
views
gb2019dm1
discretemathematics
mathematicallogic
propositionallogic
quantifiers
0
votes
1
answer
17
GATEBOOK2019DM117
Every true Indian thinks about politics and Jayaprakash Narayana thinks about politics Which of the following is valid conclusion? Jayaprakash Narayana is true Indian Jayaprakash Narayana is politician Jayaprakash Narayana is not true Indian None of the above
asked
Oct 28, 2018
in
Mathematical Logic
by
GATEBOOK
Boss
(
11.4k
points)

79
views
gb2019dm1
discretemathematics
mathematicallogic
+2
votes
1
answer
18
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 $S1 : \forall x \exists y \forall z (BF(x,y) \wedge \sim BF(x,z) \rightarrow (y \neq z))$ ... $S1$ Only $S2$ Both $S1$ and $S2$ None of the two
asked
Oct 28, 2018
in
Mathematical Logic
by
GATEBOOK
Boss
(
11.4k
points)

150
views
gb2019dm1
discretemathematics
mathematicallogic
firstorderlogic
+2
votes
1
answer
19
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) $
asked
Oct 28, 2018
in
Mathematical Logic
by
GATEBOOK
Boss
(
11.4k
points)

96
views
gb2019dm1
discretemathematics
mathematicallogic
quantifiers
0
votes
1
answer
20
GATEBOOK2019DM120
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, 2018
in
Mathematical Logic
by
GATEBOOK
Boss
(
11.4k
points)

46
views
gb2019dm1
discretemathematics
mathematicallogic
propositionallogic
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