Recent questions tagged mathematical-logic

0 votes

0 answers

1

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

0 votes

0 answers

2

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

0 votes

0 answers

3

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

+1 vote

1 answer

4

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 in Mathematical Logic by Pooja Khatri Boss (11.7k points) | 22 views

0 votes

0 answers

5

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

0 votes

0 answers

6

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

0 votes

0 answers

7

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

0 votes

0 answers

8

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

0 votes

0 answers

9

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

0 votes

0 answers

10

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

0 votes

0 answers

11

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

0 votes

0 answers

12

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

0 votes

0 answers

13

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

0 votes

0 answers

14

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

0 votes

0 answers

15

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

0 votes

0 answers

16

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

0 votes

0 answers

17

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

0 votes

0 answers

18

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

0 votes

0 answers

19

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

0 votes

0 answers

20

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

0 votes

0 answers

21

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

0 votes

0 answers

22

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

0 votes

0 answers

23

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

0 votes

0 answers

24

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

0 votes

0 answers

25

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

0 votes

0 answers

26

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

0 votes

0 answers

27

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

0 votes

0 answers

28

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

0 votes

0 answers

29

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

0 votes

0 answers

30

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

tags	tag:apple
author	user:martin
title	title:apple
content	content:apple
exclude	-tag:apple
force match	+apple
views	views:100
score	score:10
answers	answers:2
is accepted	isaccepted:true
is closed	isclosed:true

Recent questions tagged mathematical-logic

Recent Posts

Recent Blog Comments