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Recent questions tagged mathematicallogic
Webpage for Mathematical Logic
Important Question Types:
Checking validity of First Order Logic Statements
Checking validity of Propositional Logic
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CMI2019B5
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 whether @anand was ... $ 1$ : @anand once claimed that I was a knave. Chitra : Are you by any chance @anand? Suspect $1$ : Yes.
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Sep 13
in
Mathematical Logic
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gatecse
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16.6k
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cmi2019
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+2
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1
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2
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?
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Jun 4
in
Mathematical Logic
by
srestha
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117k
points)

154
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discretemathematics
mathematicallogic
+2
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1
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3
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.
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Jun 1
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Mathematical Logic
by
srestha
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117k
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60
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discretemathematics
mathematicallogic
+1
vote
1
answer
4
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
May 31
in
Mathematical Logic
by
srestha
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117k
points)

82
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mathematicallogic
discretemathematics
0
votes
1
answer
5
Proposition Logic Question
Are these propositions? 1.This sentence is true 2.This sentence is false Aren’t these liar paradox?
asked
May 30
in
Mathematical Logic
by
Reshu $ingh
(
259
points)

138
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mathematicallogic
propositionallogic
discretemathematics
+1
vote
0
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6
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’??
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May 18
in
Mathematical Logic
by
srestha
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117k
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51
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discretemathematics
mathematicallogic
firstorderlogic
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votes
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7
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
(
37
points)

63
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discretemathematics
mathematicallogic
0
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0
answers
8
Made Easy Test Series:Discrete MathMathematical 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
(
117k
points)

73
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mathematicallogic
discretemathematics
madeeasytestseries
+2
votes
1
answer
9
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
(
10.8k
points)

45
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kennethrosen
discretemathematics
mathematicallogic
propositionallogic
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votes
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answers
10
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
(
10.8k
points)

29
views
kennethrosen
discretemathematics
mathematicallogic
propositionallogic
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votes
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answers
11
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
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(
10.8k
points)

13
views
kennethrosen
discretemathematics
mathematicallogic
propositionallogic
0
votes
0
answers
12
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
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(
10.8k
points)

13
views
kennethrosen
discretemathematics
mathematicallogic
propositionallogic
0
votes
0
answers
13
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
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Apr 4
in
Mathematical Logic
by
Pooja Khatri
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(
10.8k
points)

15
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kennethrosen
discretemathematics
mathematicallogic
propositionallogic
0
votes
0
answers
14
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
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(
10.8k
points)

25
views
kennethrosen
discretemathematics
mathematicallogic
propositionallogic
0
votes
0
answers
15
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
(
10.8k
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13
views
kennethrosen
discretemathematics
mathematicallogic
propositionallogic
0
votes
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16
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
(
10.8k
points)

24
views
kennethrosen
discretemathematics
mathematicallogic
propositionallogic
0
votes
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answers
17
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); ... lefthand 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
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(
10.8k
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13
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kennethrosen
discretemathematics
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propositionallogic
0
votes
0
answers
18
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
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(
10.8k
points)

10
views
kennethrosen
discretemathematics
mathematicallogic
propositionallogic
0
votes
0
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19
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
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10.8k
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10
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kennethrosen
discretemathematics
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0
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0
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20
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
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Apr 4
in
Mathematical Logic
by
Pooja Khatri
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10.8k
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11
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kennethrosen
discretemathematics
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propositionallogic
0
votes
0
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21
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 $b$.
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Apr 4
in
Mathematical Logic
by
Pooja Khatri
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10.8k
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9
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kennethrosen
discretemathematics
mathematicallogic
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0
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0
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22
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 $n=−1$.
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Apr 4
in
Mathematical Logic
by
Pooja Khatri
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10.8k
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8
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kennethrosen
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mathematicallogic
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0
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23
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.
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Apr 4
in
Mathematical Logic
by
Pooja Khatri
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10.8k
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8
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kennethrosen
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0
votes
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24
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.
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Apr 4
in
Mathematical Logic
by
Pooja Khatri
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5
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kennethrosen
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25
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.
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Apr 4
in
Mathematical Logic
by
Pooja Khatri
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(
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kennethrosen
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0
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26
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.]
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Apr 4
in
Mathematical Logic
by
Pooja Khatri
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10.8k
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15
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kennethrosen
discretemathematics
mathematicallogic
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0
votes
0
answers
27
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
(
10.8k
points)

9
views
kennethrosen
discretemathematics
mathematicallogic
propositionallogic
0
votes
0
answers
28
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
(
10.8k
points)

11
views
kennethrosen
discretemathematics
mathematicallogic
propositionallogic
0
votes
0
answers
29
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
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(
10.8k
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11
views
kennethrosen
discretemathematics
mathematicallogic
propositionallogic
0
votes
0
answers
30
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?
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Apr 4
in
Mathematical Logic
by
Pooja Khatri
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(
10.8k
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10
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kennethrosen
discretemathematics
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