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Propositional and first order logic.
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Selfdoubt predicatelogic
Is this statement valid: $(\exists x(P(x)\rightarrow Q(x)) )\rightarrow (\exists xP(x)\rightarrow \exists xQ(x))$
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6 days
ago
in
Mathematical Logic
by
GATE_aspirant_2021
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15
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15
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firstorderlogic
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2
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
6 days
ago
in
Mathematical Logic
by
kaveeshnyk
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17
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discretemathematics
firstorderlogic
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0
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3
linear programming
asked
Apr 12
in
Mathematical Logic
by
shruti gupta1
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417
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13
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0
votes
0
answers
4
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
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10.5k
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18
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kennethrosen
discretemathematics
settheory&algebra
0
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0
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5
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
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10.5k
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11
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kennethrosen
discretemathematics
settheory&algebra
0
votes
0
answers
6
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
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(
10.5k
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3
views
kennethrosen
discretemathematics
settheory&algebra
+1
vote
1
answer
7
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
(
10.5k
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19
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kennethrosen
discretemathematics
mathematicallogic
propositionallogic
0
votes
0
answers
8
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)

61
views
propositionallogic
discretemathematics
0
votes
0
answers
9
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
(
10.5k
points)

10
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kennethrosen
discretemathematics
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0
votes
0
answers
10
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
(
10.5k
points)

8
views
kennethrosen
discretemathematics
mathematicallogic
propositionallogic
0
votes
0
answers
11
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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(
10.5k
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12
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kennethrosen
discretemathematics
mathematicallogic
propositionallogic
0
votes
0
answers
12
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
(
10.5k
points)

8
views
kennethrosen
discretemathematics
mathematicallogic
propositionallogic
0
votes
0
answers
13
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
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10.5k
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12
views
kennethrosen
discretemathematics
mathematicallogic
propositionallogic
0
votes
0
answers
14
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
(
10.5k
points)

9
views
kennethrosen
discretemathematics
mathematicallogic
propositionallogic
0
votes
0
answers
15
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
(
10.5k
points)

14
views
kennethrosen
discretemathematics
mathematicallogic
propositionallogic
0
votes
0
answers
16
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
Boss
(
10.5k
points)

9
views
kennethrosen
discretemathematics
mathematicallogic
propositionallogic
0
votes
0
answers
17
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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(
10.5k
points)

9
views
kennethrosen
discretemathematics
mathematicallogic
propositionallogic
0
votes
0
answers
18
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
(
10.5k
points)

6
views
kennethrosen
discretemathematics
mathematicallogic
propositionallogic
0
votes
0
answers
19
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
(
10.5k
points)

8
views
kennethrosen
discretemathematics
mathematicallogic
propositionallogic
0
votes
0
answers
20
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
(
10.5k
points)

7
views
kennethrosen
discretemathematics
mathematicallogic
propositionallogic
0
votes
0
answers
21
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
(
10.5k
points)

7
views
kennethrosen
discretemathematics
mathematicallogic
propositionallogic
0
votes
0
answers
22
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
(
10.5k
points)

8
views
kennethrosen
discretemathematics
mathematicallogic
propositionallogic
0
votes
0
answers
23
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
(
10.5k
points)

4
views
kennethrosen
discretemathematics
mathematicallogic
propositionallogic
0
votes
0
answers
24
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
(
10.5k
points)

7
views
kennethrosen
discretemathematics
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0
votes
0
answers
25
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
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(
10.5k
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10
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kennethrosen
discretemathematics
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0
votes
0
answers
26
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
(
10.5k
points)

7
views
kennethrosen
discretemathematics
mathematicallogic
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0
votes
0
answers
27
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
(
10.5k
points)

10
views
kennethrosen
discretemathematics
mathematicallogic
propositionallogic
0
votes
0
answers
28
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
(
10.5k
points)

10
views
kennethrosen
discretemathematics
mathematicallogic
propositionallogic
0
votes
0
answers
29
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
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Pooja Khatri
Boss
(
10.5k
points)

7
views
kennethrosen
discretemathematics
mathematicallogic
propositionallogic
0
votes
0
answers
30
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
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Pooja Khatri
Boss
(
10.5k
points)

8
views
kennethrosen
discretemathematics
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