Recent questions without an upvoted answer / GATE Overflow for GATE CSE

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8191

Kenneth Rosen Edition 7 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.

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.

Pooja Khatri

247 views

Pooja Khatri asked Apr 4, 2019

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0 answers

8192

Kenneth Rosen Edition 7 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?

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?

Pooja Khatri

211 views

Pooja Khatri asked Apr 4, 2019

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0 answers

8193

Kenneth Rosen Edition 7 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

Find a counterexample to the statement that every positive integer can be written as the sum of the squares of three integers

Pooja Khatri

334 views

Pooja Khatri asked Apr 4, 2019

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0 answers

8194

Kenneth Rosen Edition 7 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.

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...

Pooja Khatri

291 views

Pooja Khatri asked Apr 4, 2019

0 votes

0 answers

8195

Cormen Edition 3 Exercise 11.4 Question 2 (Page No. 277)
Write pseudo code for $HASH-DELETE$ as outlined in the text, and modify $HASHINSERT$ to handle the special value $DELETED.$

Write pseudo code for $HASH-DELETE$ as outlined in the text, and modify $HASHINSERT$ to handle the special value $DELETED.$

akash.dinkar12

246 views

akash.dinkar12 asked Apr 4, 2019

0 votes

0 answers

8196

Cormen Edition 3 Exercise 11.4 Question 1 (Page No. 277)
Consider inserting the keys $10, 22, 31, 4,15,28,17,88,59$ into a hash table of length $m =11$ using open addressing with the auxiliary hash function $h'(k) =k$ ... double hashing with $h_1(k) =k$ and $h_2(k)$ $=$ $1$+$($k$ $mod$ $(m-1)$)$.

Consider inserting the keys $10, 22, 31, 4,15,28,17,88,59$ into a hash table of length $m =11$ using open addressing with the auxiliary hash function $h’(k) =k$. Illust...

akash.dinkar12

470 views

akash.dinkar12 asked Apr 4, 2019

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0 answers

8197

Kenneth Rosen Edition 7 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 $p1 \leftrightarrow p3$.

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 $p1 \leftrightarrow p3$.

Pooja Khatri

234 views

Pooja Khatri asked Apr 4, 2019

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0 answers

8198

Kenneth Rosen Edition 7 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 $b=0$.

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);$0=x2−7x+6$, ...

Pooja Khatri

267 views

Pooja Khatri asked Apr 4, 2019

0 votes

0 answers

8199

Kenneth Rosen Edition 7 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 $x^2$ ... left-hand side of$x^2−1$; $x=1$ or $x=−1$,which follows because $ab=0$ implies that $a=0$ or $b=0$

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...

Pooja Khatri

269 views

Pooja Khatri asked Apr 4, 2019

0 votes

0 answers

8200

Cormen Edition 3 Exercise 11.3 Question 6 (Page No. 269)
Let $U$ be a set of $n-tuples$ of values drawn from$\mathbb{\ Z_p}$ , let $B$ $=$ $\mathbb{\ Z_p}$ , where p is prime. Define the hash function $h_b :U \rightarrow B$ for $b$ $\in$\mathbb{\ Z_p}$ on an input $ ... $\mathscr{H}$ is $n(n-1)/p$- universal according to the definition of the $\epsilon$ universal.

Let $U$ be a set of $n-tuples$ of values drawn from$\mathbb{\ Z_p}$ , let $B$ $=$ $\mathbb{\ Z_p}$ , where p is prime. Define the hash function $h_b :U \rightarrow B$ for...

akash.dinkar12

335 views

akash.dinkar12 asked Apr 4, 2019

0 votes

1 answer

8201

Kenneth Rosen Edition 7 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.

Show that these statements about the real number $x$ are equivalent:$x$ is irrational,$3x+2$ is irrational,$x/2$ is irrational.

Pooja Khatri

638 views

Pooja Khatri asked Apr 4, 2019

0 votes

0 answers

8202

Kenneth Rosen Edition 7 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.

Show that these statements about the real number $x$ are equivalent:$x$ is rational,$x/2$ is rational,$3x−1$ is rational.

Pooja Khatri

201 views

Pooja Khatri asked Apr 4, 2019

0 votes

0 answers

8203

Kenneth Rosen Edition 7 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

Show that these statements about the integer $x$ are equivalent:$3x+2$ is even,$x+5$ is odd,$x^2$ is even

Pooja Khatri

257 views

Pooja Khatri asked Apr 4, 2019

0 votes

0 answers

8204

Kenneth Rosen Edition 7 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 $b$.

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 $a$, andthe average of...

Pooja Khatri

226 views

Pooja Khatri asked Apr 4, 2019

0 votes

0 answers

8205

Kenneth Rosen Edition 7 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 $n=−1$.

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 $n=−1$.

Pooja Khatri

205 views

Pooja Khatri asked Apr 4, 2019

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0 answers

8206

Kenneth Rosen Edition 7 Exercise 1.7 Question 28 (Page No. 91)
Prove that $m^2 = n^2$ if and only if $m=n$ or m = -n.

Prove that $m^2 = n^2$ if and only if $m=n$ or m = -n.

Pooja Khatri

206 views

Pooja Khatri asked Apr 4, 2019

0 votes

0 answers

8207

Kenneth Rosen Edition 7 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.

Prove that if $n$ is a positive integer, then $n$ is odd if and only if $5n+6$ is odd.

Pooja Khatri

181 views

Pooja Khatri asked Apr 4, 2019

0 votes

0 answers

8208

Kenneth Rosen Edition 7 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.

Prove that if $n$ is a positive integer, then $n$ is even if and only if $7n+4$ is even.

Pooja Khatri

198 views

Pooja Khatri asked Apr 4, 2019

0 votes

0 answers

8209

Kenneth Rosen Edition 7 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.]

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 $...

Pooja Khatri

236 views

Pooja Khatri asked Apr 4, 2019

0 votes

0 answers

8210

Kenneth Rosen Edition 7 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.

Show that at least three of any $25$ days chosen must fall in the same month of the year.

Pooja Khatri

201 views

Pooja Khatri asked Apr 4, 2019

0 votes

0 answers

8211

Cormen Edition 3 Exercise 11.3 Question 5 (Page No. 269)
Define a family $\mathscr{H}$ of hash functions from a finite set $U$ to a finite set $B$ to be universal if for all pairs of distinct elements $k$ and $l$ in $U$, $Pr\{h(k) = h(l)\} \leq \epsilon$ where the probability is ... Show that an $\epsilon-$universal family of hash functions must have $\epsilon \geq \frac{1}{|B|} - \frac{1}{|U|}$

Define a family $\mathscr{H}$ of hash functions from a finite set $U$ to a finite set $B$ to be universal if for all pairs of distinct elements $k$ and $l$ in $U$,$Pr\{h(...

akash.dinkar12

286 views

akash.dinkar12 asked Apr 4, 2019

1 votes

0 answers

8212

Kenneth Rosen Edition 7 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.

Show that at least ten of any $64$ days chosen must fall on the same day of the week.

Pooja Khatri

215 views

Pooja Khatri asked Apr 4, 2019

0 votes

0 answers

8213

Kenneth Rosen Edition 7 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.

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.

Pooja Khatri

278 views

Pooja Khatri asked Apr 4, 2019

0 votes

0 answers

8214

Kenneth Rosen Edition 7 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?

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?

Pooja Khatri

198 views

Pooja Khatri asked Apr 4, 2019

0 votes

0 answers

8215

Kenneth Rosen Edition 7 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?

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?

Pooja Khatri

236 views

Pooja Khatri asked Apr 4, 2019

1 votes

0 answers

8216

Kenneth Rosen Edition 7 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?

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?

Pooja Khatri

261 views

Pooja Khatri asked Apr 4, 2019

0 votes

1 answer

8217

Kenneth Rosen Edition 7 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.

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.

Pooja Khatri

2.4k views

Pooja Khatri asked Apr 4, 2019

0 votes

1 answer

8218

Kenneth Rosen Edition 7 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.

Prove that if $m$ and $n$ are integers and $mn$ is even, then $m$ is even or $n$ is even.

Pooja Khatri

288 views

Pooja Khatri asked Apr 4, 2019

0 votes

1 answer

8219

Kenneth Rosen Edition 7 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 $y≥1$.

Use a proof by contraposition to show that if $x+y≥2$,where $x$ and $y$ are real numbers, then $x≥1$ or $y≥1$.

Pooja Khatri

471 views

Pooja Khatri asked Apr 4, 2019

0 votes

1 answer

8220

Cormen Edition 3 Exercise 11.3 Question 4 (Page No. 269)
Consider a hash table of size $m =1000$ and a corresponding hash function $h(k) =$ $\lfloor$ $m$($kA$ $mod$ $1$)$\rfloor$ for $A = \frac{(\sqrt{5} – 1)}{2}$ .Compute the locations to which the keys $61, 62, 63, 64,$ and $65$ are mapped.

Consider a hash table of size $m =1000$ and a corresponding hash function $h(k) =$ $\lfloor$ $m$$($$kA$ $mod$ $1$)$\rfloor$ for $A = \frac{(\sqrt{5} – 1)}{2}$ .Compute...

akash.dinkar12

559 views

akash.dinkar12 asked Apr 4, 2019

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