Recent questions and answers in Mathematical Logic

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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 5 days ago in Mathematical Logic by srestha Veteran (114k points) | 13 views

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2

self doubt consistency and satisfiability
how can we link consistency and satisfiability ? are they bidirectional? plz help

asked May 10 in Mathematical Logic by Manoj Kumar Pandey (185 points) | 14 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 in Mathematical Logic by souren (21 points) | 31 views

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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 in Mathematical Logic by srestha Veteran (114k points) | 31 views

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self doubt about maths practice
Where can i find only maths PYQ all branches . for practice ?

answered Apr 26 in Mathematical Logic by gaurav1.yuva (403 points) | 28 views

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Discrete Mathematics [Self Doubt]
Is this statement valid: $(\exists x(P(x)\rightarrow Q(x)) )\rightarrow (\exists xP(x)\rightarrow \exists xQ(x))$

asked Apr 14 in Mathematical Logic by GATE_aspirant_2021 (15 points) | 34 views

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GATE 1992
How is option (a) correct? Isn’t Universal quantifier not distributive over union/disjunction. Source: https://cse.buffalo.edu/~rapaport/191/distqfroverandor.html [closed]

asked Apr 14 in Mathematical Logic by kaveeshnyk (37 points) | 23 views

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linear programming

asked Apr 12 in Mathematical Logic by shruti gupta1 (429 points) | 15 views

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Kenneth Rosen Edition 7th Exercise 2.3 Question 51 (Page No. 154)
Show that if $x$ is a real number and $n$ is an integer, then $x<n$ if and only if $\left \lfloor x \right \rfloor < n$ $n<x$ if and only if $ n<=\left \lfloor x \right \rfloor $

asked Apr 9 in Mathematical Logic by Pooja Khatri Boss (11.7k points) | 30 views

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Kenneth Rosen Edition 7th Exercise 2.3 Question 11 (Page No. 153)
Determine whether each of these functions form $[a,b,c,d]$ to itself is onto? $f(a)=b, f(b)=a,f(c)=c,f(d)=d$ $f(a)=b, f(b)=b,f(c)=d,f(d)=c$ $f(a)=d, f(b)=b,f(c)=c,f(d)=d$

asked Apr 9 in Mathematical Logic by Pooja Khatri Boss (11.7k points) | 18 views

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Kenneth Rosen Edition 7th Exercise 2.1 Question 16 (Page No. 126)
Use a Venn diagram to illustrate the relationships $A \subset B$ and $ A \subset C.$

asked Apr 5 in Mathematical Logic by Pooja Khatri Boss (11.7k points) | 4 views

+1 vote

1 answer

12

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$} $\phi$ $\subset$ {$0$} {$0$} $\epsilon$ {$0$} {$0$} $\subset$ {$0$} {$\phi$} $\subseteq$ {$\phi$}

answered Apr 5 in Mathematical Logic by tusharp Loyal (6.5k points) | 22 views

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DDA Direct Recruitment 2019 - Asst. System Director
Which of the following gives the predicate logic representation of the sentence Ram was a man ? Ram $\rightarrow$ man $\forall x:$ Ram (x) $\rightarrow$ man (x) Man (Ram) Man $\rightarrow$ Ram I have marked option ... I want to raise an objection to this answer. Kindly provide a reliable source which confirms the correct answer for this question.

asked Apr 5 in Mathematical Logic by zeeshanmohnavi Junior (857 points) | 68 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 in Mathematical Logic by Pooja Khatri Boss (11.7k points) | 11 views

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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 in Mathematical Logic by Pooja Khatri Boss (11.7k points) | 9 views

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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 in Mathematical Logic by Pooja Khatri Boss (11.7k points) | 12 views

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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 in Mathematical Logic by Pooja Khatri Boss (11.7k points) | 8 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 in Mathematical Logic by Pooja Khatri Boss (11.7k points) | 15 views

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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 in Mathematical Logic by Pooja Khatri Boss (11.7k points) | 9 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 in Mathematical Logic by Pooja Khatri Boss (11.7k points) | 17 views

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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 in Mathematical Logic by Pooja Khatri Boss (11.7k points) | 10 views

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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 in Mathematical Logic by Pooja Khatri Boss (11.7k points) | 9 views

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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 in Mathematical Logic by Pooja Khatri Boss (11.7k points) | 8 views

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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 in Mathematical Logic by Pooja Khatri Boss (11.7k points) | 9 views

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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 in Mathematical Logic by Pooja Khatri Boss (11.7k points) | 7 views

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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 in Mathematical Logic by Pooja Khatri Boss (11.7k points) | 7 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 in Mathematical Logic by Pooja Khatri Boss (11.7k points) | 8 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 in Mathematical Logic by Pooja Khatri Boss (11.7k points) | 5 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 in Mathematical Logic by Pooja Khatri Boss (11.7k points) | 8 views

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30

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 in Mathematical Logic by Pooja Khatri Boss (11.7k points) | 11 views

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31

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 in Mathematical Logic by Pooja Khatri Boss (11.7k points) | 8 views

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32

Kenneth Rosen Edition 7th Exercise 1.7 Question 23 (Page No. 91)
Show that at least ten of any $64$ days chosen must fall on the same day of the week.

asked Apr 4 in Mathematical Logic by Pooja Khatri Boss (11.7k points) | 10 views

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33

Kenneth Rosen Edition 7th Exercise 1.7 Question 22 (Page No. 91)
Show that if you pick three socks from a drawer containing just blue socks and black socks, you must get either a pair of blue socks or a pair of black socks.

asked Apr 4 in Mathematical Logic by Pooja Khatri Boss (11.7k points) | 11 views

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Kenneth Rosen Edition 7th Exercise 1.7 Question 21 (Page No. 91)
Let $P(n)$ be the proposition “If $a$ and $b$ are positive real numbers, then $(a+b)n≥a^n+b^n.$” Prove that $P(1)$ is true. What kind of proof did you use?

asked Apr 4 in Mathematical Logic by Pooja Khatri Boss (11.7k points) | 7 views

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Kenneth Rosen Edition 7th Exercise 1.7 Question 20 (Page No. 91)
Prove the position $P(1)$, where $P(n)$ is the proposition “If $n$ is a positive integer greater than $1$, then $n^2 > n.$” What kind of proof did you use?

asked Apr 4 in Mathematical Logic by Pooja Khatri Boss (11.7k points) | 8 views

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36

Kenneth Rosen Edition 7th Exercise 1.7 Question 19 (Page No. 91)
Prove the position $P(0)$, where $P(n)$ is the proposition “If $n$ is a positive integer greater than $1$, then $n^2 > n.$” What kind of proof did you use?

asked Apr 4 in Mathematical Logic by Pooja Khatri Boss (11.7k points) | 8 views

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37

Kenneth Rosen Edition 7th Exercise 1.7 Question 17 (Page No. 91)
Show that if $n$ is an integer and $n^3+5$ is odd, then $n$ is even using. a proof by contraposition. a proof by contradiction.

asked Apr 4 in Mathematical Logic by Pooja Khatri Boss (11.7k points) | 8 views

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38

Kenneth Rosen Edition 7th Exercise 1.7 Question 16 (Page No. 91)
Prove that if $m$ and $n$ are integers and $mn$ is even, then $m$ is even or $n$ is even.

asked Apr 4 in Mathematical Logic by Pooja Khatri Boss (11.7k points) | 5 views

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39

Kenneth Rosen Edition 7th Exercise 1.7 Question 15 (Page No. 91)
Use a proof by contraposition to show that if $x+y≥2$,where $x$ and $y$ are real numbers, then $x≥1$ or $y≥1$.

asked Apr 4 in Mathematical Logic by Pooja Khatri Boss (11.7k points) | 7 views

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Kenneth Rosen Edition 7th Exercise 1.7 Question 14 (Page No. 91)
Prove that if $x$ is rational and $x\neq0$ , then $1/x$ is rational.

asked Apr 4 in Mathematical Logic by Pooja Khatri Boss (11.7k points) | 6 views

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