Recent questions tagged propositional-logic / GATE Overflow for GATE CSE

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151

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.

can this topic “PRENEX NORMAL FORM(PNF) ” is necsesary for gate or just i skip this topic.

ykrishnay

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ykrishnay asked Apr 20, 2022

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152

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 ?

49. a) Show that ∀xP (x) ∧ ∃xQ(x) is logically equivalentto ∀x∃y (P (x) ∧ Q(y)), where all quantifiers havethe same nonempty domain.b) Show that ∀xP (x) ∨...

ykrishnay

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ykrishnay asked Apr 20, 2022

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153

kenneth h rosen chapter 1 section 1.5 nested quantifiers excercise 1.5 question 48
Show that ∀xP (x) ∨ ∀xQ(x) and ∀x∀y(P (x) ∨ Q(y)), where all quantifiers have the same nonempty domain, are logically equivalent. (The new variable y is used to combine the quantifications correctly.)

Show that ∀xP (x) ∨ ∀xQ(x) and ∀x∀y(P (x) ∨ Q(y)),where all quantifiers have the same nonempty domain,are logically equivalent. (The new variable y is used to...

ykrishnay

540 views

ykrishnay asked Apr 20, 2022

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0 answers

154

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)

Find a counterexample, if possible, to these universallyquantified statements, where the domain for all variablesconsists of all integers.a) ∀x∃y(x = 1/y)b) ∀x∃y(...

ykrishnay

341 views

ykrishnay asked Apr 19, 2022

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0 answers

155

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.

Find a common domain for the variables x, y, and zfor which the statement ∀x∀y((x = y) → ∀z((z = x) ∨(z = y))) is true and another domain for which it is false....

ykrishnay

267 views

ykrishnay asked Apr 18, 2022

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156

kenneth h rosen chapter 1 section "Nested quantifers" excercise 1.5 question 26's g
Let Q(x, y) be the statement “x + y = x − y.” If the do- main for both variables consists of all integers, what are the truth values? g) ∃y∀xQ(x, y) Basically i done all the subquestions (a,b,c,d,e,f,h,i) from this question but confused in g subquestion please give answer

Let Q(x, y) be the statement “x + y = x − y.” If the do-main for both variables consists of all integers, what arethe truth values?g) ∃y∀xQ(x, y)Basically i don...

ykrishnay

200 views

ykrishnay asked Apr 18, 2022

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0 answers

157

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.

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-t...

ykrishnay

325 views

ykrishnay asked Apr 16, 2022

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0 answers

158

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.

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 er...

ykrishnay

192 views

ykrishnay asked Apr 16, 2022

10 votes

2 answers

159

GO Classes CS Test Series 2025 | Discrete Mathematics | Topic Wise Test 1 | Question: 14
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 $2^{n}$ rows in the truth table. Every row of the ... the sentence $(a \wedge b) \vee (b \wedge c)$ How many models are there for $\text{P}?$

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^{...

GO Classes

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GO Classes asked Apr 14, 2022

12 votes

1 answer

160

GO Classes CS Test Series 2025 | Discrete Mathematics | Topic Wise Test 1 | Question: 9
Many programming languages support a ternary conditional operator. For example, in $\text{C, C++},$ and $\text{Java}$, the expression $x ? y : z$ means evaluate the boolean expression $x.$ If it's true, the entire expression ... $p ? p : (\neg p)$ is tautology. $(\neg p) ? p : (\neg p)$ is tautology.

Many programming languages support a ternary conditional operator. For example, in $\text{C, C++},$ and $\text{Java}$, the expression $x ? y : z$ means “evaluate the bo...

GO Classes

419 views

GO Classes asked Apr 14, 2022

15 votes

1 answer

161

GO Classes CS Test Series 2025 | Discrete Mathematics | Topic Wise Test 1 | Question: 2
Consider the following proposition : $\text{A}_{n} = \underbrace{(p \rightarrow (q \rightarrow (p \rightarrow (q \rightarrow (\dots)))))}_{\text{number of p's + number of q's = n}}.$ Which of the following is false for ... $n > 2, \text{A}_{n}$ is Not contingency.

Consider the following proposition :$\text{A}_{n} = \underbrace{(p \rightarrow (q \rightarrow (p \rightarrow (q \rightarrow (\dots)))))}_{\text{number of p’s + number o...

GO Classes

800 views

GO Classes asked Apr 14, 2022

2 votes

2 answers

162

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 $\text{P}?$

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 ...

GO Classes

375 views

GO Classes asked Apr 14, 2022

1 votes

1 answer

163

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

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 Algor...

GO Classes

433 views

GO Classes asked Apr 14, 2022

5 votes

1 answer

164

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

Consider the following atomic propositions:$\text{R}$: It is Raining$\text{S}$: Sonu is SickWhich of the following is/are correct English Translation of the following log...

GO Classes

713 views

GO Classes asked Mar 30, 2022

5 votes

1 answer

165

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

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}) \...

GO Classes

430 views

GO Classes asked Mar 30, 2022

6 votes

1 answer

166

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 $:\neg \text{P} \vee \text{Q}$

Which of the two following propositions are equivalent in the sense that one can always be substituted for the other one in anyproposition without changing its truth valu...

GO Classes

599 views

GO Classes asked Mar 30, 2022

7 votes

1 answer

167

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 $(\text{KB} \not \models \neg \text{S})$

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.Whi...

GO Classes

520 views

GO Classes asked Mar 30, 2022

58 votes

8 answers

168

GO Classes CS 2025 | Weekly Quiz 1 | Propositional Logic | Question: 14
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 ... is her youngest child. Carl is her youngest child. Information is not sufficient to find out the youngest child.

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...

GO Classes

3.7k views

GO Classes asked Mar 30, 2022

26 votes

6 answers

169

GO Classes CS 2025 | Weekly Quiz 1 | Propositional Logic | Question: 15
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 ... Which of them is lying? The boy only The girl only Both of them Information is not sufficient to find out the liar

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.“...

GO Classes

1.6k views

GO Classes asked Mar 30, 2022

3 votes

1 answer

170

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.

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,...

GO Classes

400 views

GO Classes asked Mar 30, 2022

3 votes

0 answers

171

GO Classes 2023 | Weekly Quiz 5 | Question: 8
Consider the following arguments. $\text{Argument 1:}$ If it does not rain or it is not foggy, then the sailing race will be held, and life-saving demonstrations will go on. If the sailing race is held, then the trophy will be awarded. ... is true? Only Argument $1$ is valid. Only Argument $2$ is valid. Both Arguments are valid. No Argument is valid.

Consider the following arguments.$\text{Argument 1:}$ If it does not rain or it is not foggy, then the sailing race will be held, and life-saving demonstrations will go o...

GO Classes

706 views

GO Classes asked Mar 30, 2022

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