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Recent questions tagged propositionallogic
0
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1
answer
1
UGCNETJan2017II: 6
In propositional logic if $\left ( P \rightarrow Q \right )\wedge \left ( R \rightarrow S \right )$ and $\left ( P \vee R \right )$ are two premises such that $\begin{array}{c} (P \to Q) \wedge (R \to S) \\ P \vee R \\ \hline Y \\ \hline \end{array}$ $Y$ is the premise : $P \vee R$ $P \vee S$ $Q \vee R$ $Q \vee S$
asked
Mar 24
in
Mathematical Logic
by
jothee

69
views
ugcnetjan2017ii
discretemathematics
propositionallogic
+4
votes
3
answers
2
ISRO202073
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
isro2020
discretemathematics
mathematicallogic
propositionallogic
normal
+4
votes
3
answers
3
UGCNETJune2019II: 6
Which of the following is principal conjunctive normal form for $[(p\vee q)\wedge\ \rceil p \rightarrow \rceil q ]$ ? $p\ \vee \rceil q$ $p \vee q $ $\rceil p \vee q$ $\rceil p\ \vee \rceil q$
asked
Jul 3, 2019
in
Mathematical Logic
by
Arjun

666
views
ugcnetjune2019ii
propositionallogic
+5
votes
3
answers
4
UGCNETJune2019II: 8
Match ListI with ListII: ...  (iv); (b)  (i); (c)  (iii); (d)  (ii) (a)  (iv); (b)  (iii); (c)  (i); (d)  (ii)
asked
Jul 3, 2019
in
Mathematical Logic
by
Arjun

391
views
ugcnetjune2019ii
propositionallogic
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, 2019
in
Mathematical Logic
by
Reshu $ingh

222
views
mathematicallogic
propositionallogic
discretemathematics
+3
votes
1
answer
6
GATE2017 CE2: GA3
Four cards lie on table. Each card has a number printed on one side and a colour on the other. The faces visible on the cards are $2,3,$ red, and blue. Proposition: If a card has an even value on one side, then its opposite face is red. The card which MUST be turned over to verify the above proposition are $2,$ red $2,3,$ red $2,$ blue $2,$ red, blue
asked
May 18, 2019
in
Numerical Ability
by
Lakshman Patel RJIT

391
views
gate2017ce2
logicalreasoning
propositionallogic
+3
votes
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, 2019
in
Mathematical Logic
by
Pooja Khatri

87
views
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, 2019
in
Mathematical Logic
by
zeeshanmohnavi

107
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, 2019
in
Mathematical Logic
by
Pooja Khatri

54
views
kennethrosen
discretemathematics
mathematicallogic
propositionallogic
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, 2019
in
Mathematical Logic
by
Pooja Khatri

28
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, 2019
in
Mathematical Logic
by
Pooja Khatri

23
views
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, 2019
in
Mathematical Logic
by
Pooja Khatri

33
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, 2019
in
Mathematical Logic
by
Pooja Khatri

43
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, 2019
in
Mathematical Logic
by
Pooja Khatri

26
views
kennethrosen
discretemathematics
mathematicallogic
propositionallogic
0
votes
0
answers
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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
kennethrosen
discretemathematics
mathematicallogic
propositionallogic
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); ... 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, 2019
in
Mathematical Logic
by
Pooja Khatri

25
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, 2019
in
Mathematical Logic
by
Pooja Khatri

23
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, 2019
in
Mathematical Logic
by
Pooja Khatri

16
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, 2019
in
Mathematical Logic
by
Pooja Khatri

26
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, 2019
in
Mathematical Logic
by
Pooja Khatri

21
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, 2019
in
Mathematical Logic
by
Pooja Khatri

18
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, 2019
in
Mathematical Logic
by
Pooja Khatri

18
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, 2019
in
Mathematical Logic
by
Pooja Khatri

14
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, 2019
in
Mathematical Logic
by
Pooja Khatri

14
views
kennethrosen
discretemathematics
mathematicallogic
propositionallogic
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, 2019
in
Mathematical Logic
by
Pooja Khatri

33
views
kennethrosen
discretemathematics
mathematicallogic
propositionallogic
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, 2019
in
Mathematical Logic
by
Pooja Khatri

19
views
kennethrosen
discretemathematics
mathematicallogic
propositionallogic
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, 2019
in
Mathematical Logic
by
Pooja Khatri

18
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, 2019
in
Mathematical Logic
by
Pooja Khatri

26
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, 2019
in
Mathematical Logic
by
Pooja Khatri

20
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, 2019
in
Mathematical Logic
by
Pooja Khatri

24
views
kennethrosen
discretemathematics
mathematicallogic
propositionallogic
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