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Recent questions tagged propositional-logic
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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 ?
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Apr 20, 2022
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discrete-mathematics
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152
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.)
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discrete-mathematics
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kenneth-rosen
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153
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)
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Apr 19, 2022
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discrete-mathematics
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kenneth-rosen
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154
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.
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Apr 18, 2022
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discrete-mathematics
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kenneth-rosen
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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
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Apr 18, 2022
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156
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.
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Apr 16, 2022
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157
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.
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Apr 16, 2022
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158
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 $\text{P}?$
GO Classes
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Apr 14, 2022
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GO Classes
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goclasses_wq7
goclasses
numerical-answers
mathematical-logic
propositional-logic
2-marks
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159
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
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Apr 14, 2022
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GO Classes
420
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goclasses_wq7
goclasses
mathematical-logic
propositional-logic
2-marks
5
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160
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
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Mar 30, 2022
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GO Classes
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goclasses_wq5
goclasses
mathematical-logic
propositional-logic
multiple-selects
1-mark
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161
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
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Mar 30, 2022
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GO Classes
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goclasses_wq5
goclasses
mathematical-logic
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6
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162
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 $:\neg \text{P} \vee \text{Q}$
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Mar 30, 2022
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575
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goclasses_wq5
goclasses
mathematical-logic
propositional-logic
multiple-selects
1-mark
7
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163
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
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Mar 30, 2022
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GO Classes
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goclasses_wq5
goclasses
mathematical-logic
propositional-logic
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2-marks
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164
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
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Mar 30, 2022
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383
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goclasses_wq5
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mathematical-logic
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1-mark
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165
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.
GO Classes
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Mar 30, 2022
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goclasses_wq5
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mathematical-logic
propositional-logic
2-marks
6
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166
GO Classes 2023 | Weekly Quiz 5 | Question: 9
Consider the following puzzle. Five persons $\text{A, B, C, D, E}$ are in a compartment in a train. $\text{A, C, E}$ are men, and $\text{B, D}$ ... given above, $4$ are true, and $4$ are false. Who is the murderer (Assume exactly one person is the murderer)? A B C D
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