Recent questions tagged mathematical-logic - GATE Overflow

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UGCNET-Jan2017-III: 59
Which of the following statements is true? The sentence $S$ is a logical consequence of $S_{1},\dots,S_{n}$ if and only if $S_{1}\wedge S_{2} \wedge \dots \wedge S_{n}\rightarrow S$ is satisfiable. The sentence $S$ ... of $S_{1},\dots,S_{n}$ if and only if $S_{1}\wedge S_{2}\wedge \dots \wedge S_{n}\wedge S$ is inconsistent.

asked Mar 24 in Discrete Mathematics by jothee | 59 views

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2 answers

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UGCNET-Jan2017-II: 2
Match the following : ...

asked Mar 24 in Mathematical Logic by jothee | 75 views

+4 votes

3 answers

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ISRO2020-73
Given that $B(a)$ means “$a$ is a bear” $F(a)$ means “$a$ is a fish” and $E(a,b)$ means “$a $ eats $b$” Then what is the best meaning of $\forall x [F(x) \to \forall y(E(y,x)\rightarrow b(y))]$ Every fish is eaten by some bear Bears eat only fish Every bear eats fish Only bears eat fish

asked Jan 13 in Mathematical Logic by Satbir | 497 views

+1 vote

1 answer

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CMI2019-B-5
In the land of Twitter, there are two kinds of people: knights (also called outragers), who always tell the truth, and knaves (also called trolls), who always lie. It so happened that a person with handle @anand tweeted something offensive. It was not known ... $3:$ My lawyer always tells the truth. Which of the above suspects are innocent, and which are guilty? Explain your reasoning.

asked Sep 14, 2019 in Mathematical Logic by gatecse | 123 views

+3 votes

1 answer

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Mathematical Logic Ques:Self doubt
“Not every satisfiable logic is valid” Representation of it will be $1)\sim \left ( \forall S(x)\rightarrow V(x) \right )$ or $2)\sim \left ( \forall S(x)\vee V(x) \right )$ Among $1)$ and $2)$, which one is correct? and why?

asked Jun 5, 2019 in Mathematical Logic by srestha | 246 views

+2 votes

1 answer

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Doubt on GATE Question
Read the statements: All women are entrepreneurs. Some women are doctors. Which of the following conclusions can be logically inferred from the above statements? All women are doctors All doctors are entrepreneurs All entrepreneurs are women Some entrepreneurs are doctors ... Is it because , if we make set of doctor as 0, then All doctors are entrepreneurs is meaningless.

asked Jun 1, 2019 in Mathematical Logic by srestha | 115 views

+1 vote

1 answer

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Mathematical Logic: Doubt on meaning of statement
The notation $\exists ! x P(x)$ denotes the proposition there exists a unique $x$ such that $P(x)$ ... What will be answer here?? Is the assumption only for left hand side and not right hand side??

asked Jun 1, 2019 in Mathematical Logic by srestha | 148 views

0 votes

1 answer

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Proposition Logic Question
Are these propositions? 1.This sentence is true 2.This sentence is false Aren’t these liar paradox?

asked May 30, 2019 in Mathematical Logic by Reshu $ingh | 222 views

+1 vote

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Self Doubt:Mathematical Logic
Represent these two statement in first order logic: $A)$ Only Alligators eat humans $B)$ Every Alligator eats humans Is Every represents $\equiv \exists$ and Only represents $\equiv \forall$ ?? Can we differentiate it with verb ‘eat’ and ‘eats’??

asked May 18, 2019 in Mathematical Logic by srestha | 115 views

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Discrete mathematics and its application 7th ed - Kenneth H. Rosen
Do i have to study the whole chapter Logics and Proofs in Discrete mathematics and its applications by Kenneth H. Rosen if not upto which portion should i study.

asked May 1, 2019 in Mathematical Logic by souren | 145 views

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0 answers

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Made Easy Test Series:Discrete Math-Mathematical Logic
Consider the following first order logic statement $I)\forall x\forall yP\left ( x,y \right )$ $II)\forall x\exists yP\left ( x,y \right )$ $III)\exists x\exists yP\left ( x,y \right )$ $III)\exists x\forall yP\left ( x,y \right )$ Which one ... true , then $III),IV)$ is true $B)$ If $IV)$ is true , then $II),III)$ is true $C)$ None of these

asked Apr 27, 2019 in Mathematical Logic by srestha | 117 views

+3 votes

1 answer

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Kenneth Rosen Edition 7th Exercise 2.1 Question 9 (Page No. 125)
Determine whether each of these statements is true or false. $0$ $ \epsilon$ $\phi$ $\phi$ $\epsilon$ {$0$} {$0$} $ \subset$ {$ \phi$} $\phi$ $\subset$ {$0$} {$0$} $\epsilon$ {$0$} {$0$} $\subset$ {$0$} {$\phi$} $\subseteq$ {$\phi$}

asked Apr 5, 2019 in Mathematical Logic by Pooja Khatri | 87 views

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Kenneth Rosen Edition 7th Exercise 1.7 Question 42 (Page No. 92)
Prove that these four statements about the integer $n$ are equivalent: $n^2$is odd, $1−n$ is even, $n^3$ is odd, $n^2+1$ is even.

asked Apr 4, 2019 in Mathematical Logic by Pooja Khatri | 53 views

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0 answers

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Kenneth Rosen Edition 7th Exercise 1.7 Question 41 (Page No. 92)
Prove that if $n$ is an integer, these four statements are equivalent: $n$ is even, $n+1$ is odd, $3n+1$isodd, $3n$ is even.

asked Apr 4, 2019 in Mathematical Logic by Pooja Khatri | 28 views

0 votes

0 answers

15

Kenneth Rosen Edition 7th Exercise 1.7 Question 39 (Page No. 92)
Prove that at least one of the real numbers $a_1,a_2,...,a_n$ is greater than or equal to the average of these numbers.What kind of proof did you use?

asked Apr 4, 2019 in Mathematical Logic by Pooja Khatri | 23 views

0 votes

0 answers

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Kenneth Rosen Edition 7th Exercise 1.7 Question 38 (Page No. 92)
Find a counterexample to the statement that every positive integer can be written as the sum of the squares of three integers

asked Apr 4, 2019 in Mathematical Logic by Pooja Khatri | 33 views

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Kenneth Rosen Edition 7th Exercise 1.7 Question 37 (Page No. 91)
Show that the propositions $p1,p2,p3,p4,$ and $p5$ can be shown to be equivalent by proving that the conditional statements $p1 \rightarrow p4$ , $p3 \rightarrow p1$ ,$p4 \rightarrow p2$ ,$p2 \rightarrow p5$, and $p5 \rightarrow p3$ are true.

asked Apr 4, 2019 in Mathematical Logic by Pooja Khatri | 43 views

0 votes

0 answers

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Kenneth Rosen Edition 7th Exercise 1.7 Question 36 (Page No. 91)
Show that the propositions $p1,p2,p3$, and $p4$can be shown to be equivalent by showing that $p1 \leftrightarrow p4,p2 \leftrightarrow p3$, and $p1 \leftrightarrow p3$.

asked Apr 4, 2019 in Mathematical Logic by Pooja Khatri | 26 views

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Kenneth Rosen Edition 7th Exercise 1.7 Question 35 (Page No. 91)
Are these steps for finding the solutions of $\sqrt{x+3=3−x}$ correct? $\sqrt{x+3=3−x}$ is given; $x+3=x2−6x+9$, obtained by squaring both sides of(1); $0=x2−7x+6$, obtained by subtracting $x+3$ from both sides of(2); $0=(x−1)(x−6)$, ... -hand side of(3); $x=1$ or $x=6$,which follows from(4) because $ab=0$ implies that $a=0$ or $b=0$.

asked Apr 4, 2019 in Mathematical Logic by Pooja Khatri | 38 views

0 votes

0 answers

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Kenneth Rosen Edition 7th Exercise 1.7 Question 34 (Page No. 91)
Is this reasoning for finding the solutions of the equation $\sqrt{2x^2−1=x}$ correct? $\sqrt{2x^2−1=x}$ is given; $2x^2−1=x^2$, obtained by squaring both sides of (1); $x^2−1=0$, obtained by subtracting $x^2$from both sides of (2); ... left-hand side of$x^2−1$; $x=1$ or $x=−1$,which follows because $ab=0$ implies that $a=0$ or $b=0$

asked Apr 4, 2019 in Mathematical Logic by Pooja Khatri | 25 views

0 votes

0 answers

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Kenneth Rosen Edition 7th Exercise 1.7 Question 33 (Page No. 91)
Show that these statements about the real number $x$ are equivalent: $x$ is irrational, $3x+2$ is irrational, $x/2$ is irrational.

asked Apr 4, 2019 in Mathematical Logic by Pooja Khatri | 23 views

0 votes

0 answers

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Kenneth Rosen Edition 7th Exercise 1.7 Question 32 (Page No. 91)
Show that these statements about the real number $x$ are equivalent: $x$ is rational, $x/2$ is rational, $3x−1$ is rational.

asked Apr 4, 2019 in Mathematical Logic by Pooja Khatri | 16 views

0 votes

0 answers

23

Kenneth Rosen Edition 7th Exercise 1.7 Question 31 (Page No. 91)
Show that these statements about the integer $x$ are equivalent: $3x+2$ is even, $x+5$ is odd, $x^2$ is even

asked Apr 4, 2019 in Mathematical Logic by Pooja Khatri | 26 views

0 votes

0 answers

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Kenneth Rosen Edition 7th Exercise 1.7 Question 30 (Page No. 91)
Show that these three statements are equivalent, where $a$ and $b$ are real numbers: $a$ is less than $b$, the average of $a$ and $b$ is greater than $a$, and the average of $a$ and $b$ is less than $b$.

asked Apr 4, 2019 in Mathematical Logic by Pooja Khatri | 21 views

0 votes

0 answers

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Kenneth Rosen Edition 7th Exercise 1.7 Question 29 (Page No. 91)
Prove or disprove that if $m$ and $n$ are integers such that $mn=1$, then either $m=1$ and $n=1$, or else $m=−1$ and $n=−1$.

asked Apr 4, 2019 in Mathematical Logic by Pooja Khatri | 18 views

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Kenneth Rosen Edition 7th Exercise 1.7 Question 28 (Page No. 91)
Prove that $m^2 = n^2$ if and only if $m=n$ or m = -n.

asked Apr 4, 2019 in Mathematical Logic by Pooja Khatri | 18 views

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Kenneth Rosen Edition 7th Exercise 1.7 Question 27 (Page No. 91)
Prove that if $n$ is a positive integer, then $n$ is odd if and only if $5n+6$ is odd.

asked Apr 4, 2019 in Mathematical Logic by Pooja Khatri | 14 views

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Kenneth Rosen Edition 7th Exercise 1.7 Question 26 (Page No. 91)
Prove that if $n$ is a positive integer, then $n$ is even if and only if $7n+4$ is even.

asked Apr 4, 2019 in Mathematical Logic by Pooja Khatri | 14 views

0 votes

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Kenneth Rosen Edition 7th Exercise 1.7 Question 25 (Page No. 91)
Use a proof by contradiction to show that there is no rational number $r$ for which $r^3+r+1=0$. [Hint:Assume that $r=a/b$ is a root, where $a$ and $b$ are integers and $a/b$ is in lowest terms. Obtain an equation involving integer $s$ by multiplying by $b^3$. Then look at whether $a$ and $b$ are each odd or even.]

asked Apr 4, 2019 in Mathematical Logic by Pooja Khatri | 33 views

0 votes

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Kenneth Rosen Edition 7th Exercise 1.7 Question 24 (Page No. 91)
Show that at least three of any $25$ days chosen must fall in the same month of the year.

asked Apr 4, 2019 in Mathematical Logic by Pooja Khatri | 19 views

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