Recent questions and answers in Mathematical Logic

Recent questions and answers in Mathematical Logic

2 votes

3 answers

1

GO Classes Weekly Quiz 2 | Programming in C | Propositional Logic | Question: 6
Let $p$ be the statement Maria learns discrete mathematics and $q$ the statement Maria will find a good job. Which of the following English Statement expresses the statement $p \rightarrow q$ ? If Maria learns ... good job. For Maria to get a good job, it is sufficient for her to learn discrete mathematics.

samarpita answered in Mathematical Logic 4 days ago

35 views

0 votes

2 answers

2

No of solution of the given equation
The Number of Points $x \in \Re$ for which $\sin ^{2} x-3x=5$ is , 0 1 more than one but finite $\infty$

Amar45 answered in Mathematical Logic 6 days ago

by Amar45

38 views

0 votes

1 answer

3

can any one suggest resources for discrete mathematics for gate
suggest some good resources for discrete mathematics

Bharat Bhushan answered in Mathematical Logic May 11

by Bharat Bhushan

49 views

1 vote

2 answers

4

GO Classes Weekly Quiz 2 | Programming in C | Propositional Logic | Question: 11

vansh03 answered in Mathematical Logic May 9

28 views

1 vote

1 answer

5

GO Classes Weekly Quiz 2 | Programming in C | Propositional Logic | Question: 4
How many rows appear in a truth table for this compound proposition? $p \rightarrow \neg p$

GO Classes answered in Mathematical Logic May 2

26 views

1 vote

1 answer

6

GO Classes Weekly Quiz 2 | Programming in C | Propositional Logic | Question: 5
How many rows appear in a truth table for this compound proposition? $(p \wedge r \wedge t) \leftrightarrow (q \wedge t)$

GO Classes answered in Mathematical Logic May 2

19 views

4 votes

5 answers

7

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

Vishalk17 answered in Mathematical Logic May 1

3.2k views

73 votes

7 answers

8

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 ___________.

Vishalk17 answered in Mathematical Logic Apr 30

13.3k views

0 votes

1 answer

9

kenneth h rosen chapter 1 section 1.5 PRENEX NORMAL FORM in excercise 1.5
can this topic “PRENEX NORMAL FORM(PNF) ” is necsesary for gate or just i skip this topic.

mahendrapatel answered in Mathematical Logic Apr 20

by mahendrapatel

35 views

0 votes

0 answers

10

kenneth h rosen chapter 1 section section 1.5 nested quatnifiers excercise 49
49. a) Show that ∀xP (x) ∧ ∃xQ(x) is logically equivalent to ∀x∃y (P (x) ∧ Q(y)), where all quantifiers have the same nonempty domain. b) Show that ∀xP (x) ∨ ∃xQ(x) is equivalent to ∀x∃y (P (x) ∨ Q(y)), where all quantifiers have the same nonempty domain. please anybody tell how to prove this logical equivalency ?

ykrishnay asked in Mathematical Logic Apr 20

46 views

28 votes

7 answers

11

GATE CSE 1991 | Question: 03,xii
If $F_1$, $F_2$ and $F_3$ are propositional formulae such that $F_1 \land F_2 \rightarrow F_3$ and $F_1 \land F_2 \rightarrow \sim F_3$ are both tautologies, then which of the following is true: Both $F_1$ and $F_2$ are tautologies The conjunction $F_1 \land F_2$ is not satisfiable Neither is tautologous Neither is satisfiable None of the above

Deepak Poonia answered in Mathematical Logic Apr 20

by Deepak Poonia

5.0k views

0 votes

0 answers

12

kenneth h rosen chapter 1 section 1.5 nested quantifiers excercise 1.5 question 48

ykrishnay asked in Mathematical Logic Apr 20

56 views

0 votes

0 answers

13

kenneth h rosen chapter 1 section nested quantifers excercise 1.5 question 40
Find a counterexample, if possible, to these universally quantified statements, where the domain for all variables consists of all integers. a) ∀x∃y(x = 1/y) b) ∀x∃y(y^2 − x < 100)

ykrishnay asked in Mathematical Logic Apr 19

38 views

2 votes

2 answers

14

GO Classes 2023 | Weekly Quiz 7 | Question: 3
Let $\text{P}$ be a compound proposition over $4$ propositional variables $: a,b,c,d.$ We know that for $a$ compound proposition over $n$ propositional variables, we have $2^{n}$ ... is true for that row. Let $\text{P}$ be $a \leftrightarrow b$ How many models are there for $\text{P}?$

diptanshu malviya answered in Mathematical Logic Apr 19

by diptanshu malviya

85 views

0 votes

0 answers

15

kenneth h rosen chapter 1 section 1.5 nested quantifers question 34
Find a common domain for the variables x, y, and z for which the statement ∀x∀y((x = y) → ∀z((z = x) ∨ (z = y))) is true and another domain for which it is false.

ykrishnay asked in Mathematical Logic Apr 18

43 views

0 votes

0 answers

16

kenneth h rosen chapter 1 section "Nested quantifers" excercise 1.5 question 26's g

ykrishnay asked in Mathematical Logic Apr 18

35 views

0 votes

0 answers

17

kenneth h rosen chapter 1 section 1.5 excercise 1.5 question 18 e
Express each of these system specifications using predi- cates, quantifiers, and logical connectives, if necessary. e) No one knows the password of every user on the sys- tem except for the system administrator, who knows all passwords.

ykrishnay asked in Mathematical Logic Apr 16

48 views

0 votes

0 answers

18

kenneth h rosen chapter 1 section 1.5 nested quantifiers excercise no 17, b
Express each of these system specifications using predi- cates, quantifiers, and logical connectives, if necessary. b)There is a process that continues to run during all error conditions only if the kernel is working correctly.

ykrishnay asked in Mathematical Logic Apr 16

24 views

2 votes

1 answer

19

GO Classes 2023 | Weekly Quiz 7 | Question: 1
Let $\text{M}(x)$ denote the predicate $x$ is a mobile ; $\text{B}(x)$ denote the predicate $x$ is black ; $\text{C}(x)$ denote the predicate $x$ has calculator . Suppose that the universe is set of all mobiles. Which of the following ... $: \forall x ( \text{M}(x) \wedge \text{C}(x) )$

shishir__roy answered in Mathematical Logic Apr 14

by shishir__roy

224 views

1 vote

1 answer

20

GO Classes 2023 | Weekly Quiz 7 | Question: 6
Consider the following logical inferences : $\text{S1} :$ If I study Discrete Mathematics, then I will study Computer Science. If I study C, then I will study Algorithms. Therefore, If I study Discrete Mathematics or C then I will study ... correct but $\text{S2}$ is a correct inference Both $\text{S1}$ and $\text{S2}$ are not correct inferences

shishir__roy answered in Mathematical Logic Apr 14

by shishir__roy

62 views

2 votes

2 answers

21

GO Classes 2023 | Weekly Quiz 7 | Question: 4
Consider the following statement $\text{S}$ in an universe $\text{U}.$ $\text{S} : \forall x \forall y (x = y)$ What is the maximum cardinality of $\text{U}$ such that $\text{S}$ is true?

sahanashenoy answered in Mathematical Logic Apr 14

by sahanashenoy

95 views

1 vote

1 answer

22

GO Classes 2023 | Weekly Quiz 7 | Question: 2
Let the universe be the set of all integers. Which of the following statements is/are true? (Where “$+$” is the integer addition) $\forall x \forall y \exists z (x+y = z)$ $\forall x \exists y \forall z (x+y = z)$ $\exists x \forall y \exists z (x+y = z)$ $\exists z \forall x \exists y (x+y = z)$

shishir__roy answered in Mathematical Logic Apr 14

by shishir__roy

75 views

1 vote

1 answer

23

GO Classes 2023 | Weekly Quiz 7 | Question: 8
Consider the formula $\exists x \exists y \exists z(\text{R}(x, y) \wedge \text{R}(z, y) \wedge \text{R}(x, z) \wedge \neg \text{R}(z, x)).$ For which of the following interpretations, is this formula true? $(\text{N}$ ... $\text{R}(x,y) : y = x0 \;\text{or}\; y = x1.$

shishir__roy answered in Mathematical Logic Apr 14

by shishir__roy

67 views

0 votes

2 answers

24

kenneth h rosen chapter 1 excercise 1.3
Show that (p → q) ∧ (q → r) and (p → r) is a logically equivalent to each other

Am607 answered in Mathematical Logic Apr 13

by Am607

151 views

0 votes

0 answers

25

About set identities
Does associative properties follows only when all the operators in the given expression same (union or intersection) or it do follows when there are different symbols present in the given expression. E.g. a U (b U c) U d = a U b U (c U d) ; (a U b) /\ c U d = a U (b /\ c) U d.

Udit Narayan asked in Mathematical Logic Apr 9

by Udit Narayan

27 views

0 votes

0 answers

26

How many multisets can be constructed from n distinct elements? if n bounded.
How many multisets can be constructed from n distinct elements? if n bounded. according to me it will be 2^n. is it correct?

Biswarup01 asked in Mathematical Logic Apr 6

35 views

1 vote

1 answer

27

GO Classes 2023 | Weekly Quiz 3 | Question: 21
Of all the connectives we've seen, the implication $\rightarrow$ connective is probably the trickiest. Let $F$ and $G$ be two propositional formulas, over same set of propositional variables, such that $(F \rightarrow G)$ ... $(F \rightarrow G)\wedge (G \rightarrow F)$ is necessarily a Tautology. $F$ is necessarily equivalent to $G.$

sayantanb211 answered in Mathematical Logic Apr 5

by sayantanb211

71 views

2 votes

3 answers

28

GO Classes 2023 | Weekly Quiz 3 | Question: 11
Let $P$ be a compound proposition over $4$ propositional variables: $a,b,c,d$. We know that for a compound proposition over $n$ propositional variables, we have $2^n$ rows in the truth table. Every row of truth table of $P$ is called an ... $P$ be $"a \rightarrow b"$. How many models are there for $P$ ?

Amar45 answered in Mathematical Logic Apr 3

by Amar45

220 views

0 votes

5 answers

29

NIELIT 2016 MAR Scientist C - Section C: 65
In propositional logic, which of the following is equivalent to $p \rightarrow q$? $\sim p\rightarrow q$ $ \sim p \vee q$ $ \sim p \vee \sim q$ $p\rightarrow \sim q$

Vishalk17 answered in Mathematical Logic Apr 1

1.3k views

19 votes

8 answers

30

GATE CSE 1987 | Question: 10e
Show that the conclusion $(r \to q)$ follows from the premises$:p, (p \to q) \vee (p \wedge (r \to q))$

Vishalk17 answered in Mathematical Logic Apr 1

2.7k views

38 votes

6 answers

31

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 $d$

sameer_hack answered in Mathematical Logic Apr 1

8.8k views

1 vote

1 answer

32

GO Classes 2023 | Weekly Quiz 3 | Question: 14
If $F1, F2$ and $F3$ are propositional formulae/expressions, over same set of propositional variables, such that $F1 \wedge F2 \wedge F3$ is unsatisfiable and such that the conjunction of any pair of them is satisfiable, then which of the ... $(F1\rightarrow F2),(F2\rightarrow F3),(F3\rightarrow F1)$, all are contingency.

shaad_iqbal answered in Mathematical Logic Mar 31

92 views

3 votes

1 answer

33

GO Classes 2023 | Weekly Quiz 5 | Question: 12
Let $\alpha, \beta $ be two propositional formulas. Which of the following assertions is true? $\alpha \models \beta$ if and only if the sentence $(\alpha \wedge \neg \beta)$ is unsatisfiable. If $\alpha\models \gamma $ ... $\alpha \models(\beta \vee \gamma)$ then $\alpha \models \beta $ or $\alpha \models \gamma $ (or both).

neel19 answered in Mathematical Logic Mar 31

by neel19

156 views

4 votes

1 answer

34

GO Classes 2023 | Weekly Quiz 5 | Question: 1
Consider the following atomic propositions: $\text{R}$: It is Raining $\text{S}$ ... is raining, and vice versa It is raining is equivalent to sonu is sick It is raining or sonu is sick but not both

GO Classes answered in Mathematical Logic Mar 30

148 views

4 votes

1 answer

35

GO Classes 2023 | Weekly Quiz 5 | Question: 2
Let $\text{P}$ be a propositional variable. Which of the following propositions are tautologies? $\text{P}$ $\text{P} \Rightarrow \text{P}$ $(\text{P} \Rightarrow \text{P}) \Rightarrow \text{P}$ $\text{P} \Rightarrow(\text{P} \Rightarrow \text{P})$

GO Classes answered in Mathematical Logic Mar 30

82 views

5 votes

1 answer

36

GO Classes 2023 | Weekly Quiz 5 | Question: 3
Which of the two following propositions are equivalent in the sense that one can always be substituted for the other one in any proposition without changing its truth value? first proposition $:\text{P} \Rightarrow \text{Q};$ ... $:\neg \text{P};$ second proposition $:\neg \text{P} \vee \text{Q}$

GO Classes answered in Mathematical Logic Mar 30

75 views

4 votes

1 answer

37

GO Classes 2023 | Weekly Quiz 5 | Question: 4
Let $\text{ KB }$ stand for $\text{ knowledge base }$ which is a set of premises/statements, as mentioned following: Let $\text{S}$ be a propositional formula. Which of the following is $\text{ possible }$? $(\text{KB}\models \text{S})$ ... $(\text{KB} \models \text{S})$ and $(\text{KB} \not \models \neg \text{S})$

GO Classes answered in Mathematical Logic Mar 30

113 views

3 votes

1 answer

38

GO Classes 2023 | Weekly Quiz 5 | Question: 5
Consider the following popular puzzle. When asked for the ages of her three children, Mrs. Baker says that Alice is her youngest child if Bill is not her youngest child, and that. Alice is not her youngest child if Carl is not ... . Bill is her youngest child. Carl is her youngest child. Information is not sufficient to find out the youngest child.

GO Classes answered in Mathematical Logic Mar 30

72 views

4 votes

1 answer

39

GO Classes 2023 | Weekly Quiz 5 | Question: 6
Consider the following popular puzzle. A boy and a girl are talking. One of them has black hair, another has white hair. I am a boy said the child with black hair. I am a girl said the child with white hair. At least one of ... lying. Which of them is lying? The boy only The girl only Both of them Information is not sufficient to find out the liar

GO Classes answered in Mathematical Logic Mar 30

82 views

2 votes

0 answers

40

GO Classes 2023 | Weekly Quiz 5 | Question: 7
Consider the following arguments. $\text{Argument 1:}$ Kerry errs or Myrna fails to show. If Kerry errs, then he does not break the record. Myrna fails to show. Therefore, Kerry does break the record. $\text{Argument 2:}$ If Tasha leaves, ... is true? Only Argument $1$ is valid. Only Argument $2$ is valid. Both Arguments are valid. No Argument is valid.

GO Classes asked in Mathematical Logic Mar 30

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