Hot questions in Engineering Mathematics / GATE Overflow for GATE CSE

1 votes

1 answer

3461

Kenneth Rosen Edition 7 Exercise 1.3 Question 9 (Page No. 35)
Show that each of these conditional statements is a tautology by using truth tables. $(p \wedge q) \rightarrow p $ $ p \rightarrow (p \vee q)$ $\sim p \rightarrow (p \rightarrow q)$ $(p\wedge q)\rightarrow (p \rightarrow q)$ $\sim (p \rightarrow q) \rightarrow p$ $\sim(p \rightarrow p) \rightarrow \sim q$

Show that each of these conditional statements is a tautology by using truth tables.$(p \wedge q) \rightarrow p $$ p \rightarrow (p \vee q)$$\sim p \rightarrow (p \righta...

Pooja Khatri

1.4k views

Pooja Khatri asked Mar 15, 2019

0 votes

0 answers

3462

Kenneth Rosen Edition 7 Exercise 2.3 Question 2 (Page No. 152)
Determine whether $f$ is a function from $Z$ to $R$ if $f(n) = +-n.$ $f(n) = \sqrt{n^2+1}.$ $f(n) = 1/(n^2-4).$

Determine whether $f$ is a function from $Z$ to $R$ if$f(n) = +-n.$$f(n) = \sqrt{n^2+1}.$$f(n) = 1/(n^2-4).$

Pooja Khatri

256 views

Pooja Khatri asked Apr 9, 2019

1 votes

0 answers

3463

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

217 views

Pooja Khatri asked Apr 4, 2019

0 votes

0 answers

3464

Kenneth Rosen Edition 7 Exercise 2.3 Question 38 (Page No. 154)
Let $f(x) = ax+b$ and $g(x) =cx+d$, where a,b,c, and d ar constants. Determine neccessary and sufficient conditions on the constants a,b,c, and d so that $fog =gof$

Let $f(x) = ax+b$ and $g(x) =cx+d$, where a,b,c, and d ar constants. Determine neccessary and sufficient conditions on the constants a,b,c, and d so that $fog =gof$

Pooja Khatri

185 views

Pooja Khatri asked Apr 9, 2019

1 votes

2 answers

3465

GATE Overflow | Mathematics | Test 1 | Question: 1
A relation $R$ is defined as $xRy$ , if $x$ and $y$ are NOT equal. This relation $R$ is symmetric but not reflexive symmetric and transitive but not reflexive an equivalent relation none of reflexive or symmetric or transitive

A relation $R$ is defined as $xRy$ , if $x$ and $y$ are NOT equal. This relation $R$ issymmetric but not reflexivesymmetric and transitive but not reflexivean equivalent ...

Bikram

734 views

Bikram asked Aug 6, 2016

0 votes

0 answers

3466

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

271 views

Pooja Khatri asked Apr 4, 2019

0 votes

0 answers

3467

Kenneth Rosen Edition 7 Exercise 2.3 Question 47 Page No. 154)
Show that $\left \lceil x-1/2 \right \rceil$ is the closest integer to the number $x$,except when $x$ is midway between two integers, when it is the smaller of these two integers

Show that $\left \lceil x-1/2 \right \rceil$ is the closest integer to the number $x$,except when $x$ is midway between two integers, when it is the smaller of these two ...

Pooja Khatri

186 views

Pooja Khatri asked Apr 9, 2019

3 votes

1 answer

3468

JEST Sample Question 1-b
When is the following statement true? (A ∪ B) ∩ C = A ∩ C (A) If Ā ∩ B ∩ C = φ (B) If A ∩ B ∩ C = φ (C) always (D) never

When is the following statement true? (A ∪ B) ∩ C = A ∩ C(A) If Ā ∩ B ∩ C = φ(B) If A ∩ B ∩ C = φ(C) always(D) never

sripo

856 views

sripo asked Feb 15, 2019

0 votes

0 answers

3469

Kenneth Rosen Edition 7 Exercise 2.3 Question 1 (Page No. 152)
Why is $f$ not a function from $R$ to $R$ if $f(x) =1 /x?$ $f(x) = \sqrt{x} ?$ $f(x) =± \sqrt{(x^2+1)}? $

Why is $f$ not a function from $R$ to $R$ if$f(x) =1 /x?$$f(x) = \sqrt{x} ?$$f(x) =± \sqrt{(x^2+1)}? $

Pooja Khatri

252 views

Pooja Khatri asked Apr 9, 2019

0 votes

1 answer

3470

Kenneth Rosen Edition 7 Exercise 2.1 Question 11 (Page No. 125)
Determine whether each of these statements is true or false. $x$ $\epsilon$ {$x$} {$x$} $\subset$ {$x$} {$x$} $\epsilon$ {$x$} {$x$} $\epsilon$ {{$x$}} $\phi$ $\subseteq$ {$x$} $\phi$ $\epsilon$ {$x$}

Determine whether each of these statements is true or false.$x$ $\epsilon$ {$x$}{$x$} $\subset$ {$x$}{$x$} $\epsilon$ {$x$}{$x$} $\epsilon$ {{$x$}}$\phi$ $\subseteq$ {$x$...

Pooja Khatri

265 views

Pooja Khatri asked Apr 5, 2019

0 votes

0 answers

3471

Kenneth Rosen Edition 7 Exercise 2.1 Question 44 (Page No. 126)
Find the truth set of each of these predicates where the domain is the set of integers. $P(x) : x^3>=1$ $Q(x) : x^2=2$ $R(x) : x<x^2$

Find the truth set of each of these predicates where the domain is the set of integers.$P(x) : x^3>=1$$Q(x) : x^2=2$$R(x) : x<x^2$

Pooja Khatri

270 views

Pooja Khatri asked Apr 5, 2019

0 votes

0 answers

3472

Kenneth Rosen Edition 7 Exercise 2.3 Question 53 (Page No. 154)
Prove that if $n$ is an integer, then $\left \lfloor n/2 \right \rfloor = n/2$ if $n$ is even and $(n-1)/2$ if $n$ is odd.

Prove that if $n$ is an integer, then $\left \lfloor n/2 \right \rfloor = n/2$ if $n$ is even and $(n-1)/2$ if $n$ is odd.

Pooja Khatri

187 views

Pooja Khatri asked Apr 9, 2019

1 votes

0 answers

3473

Kenneth Rosen Edition 7 Exercise 2.1 Question 13 (Page No. 126)
Use a Venn diagram to illustrate the set of all months of the year whose names do not contain the letter $R$ in the set of all months of the year.

Use a Venn diagram to illustrate the set of all months of the year whose names do not contain the letter $R$ in the set of all months of the year.

Pooja Khatri

266 views

Pooja Khatri asked Apr 5, 2019

0 votes

0 answers

3474

Kenneth Rosen Edition 7 Exercise 1.6 Question 4 (Page No. 78)
What rule of inference is used in each of these arguments? Kangaroos live in Australia and are marsupials. There-fore, kangaroos are marsupials. It is either hotter than 100 degrees today or the pollution is dangerous. It ... understand the material . Therefore ,If I work all night on this homework, Then I will understand the material.

What rule of inference is used in each of these arguments?Kangaroos live in Australia and are marsupials. There-fore, kangaroos are marsupials.It is either hotter than 10...

Pooja Khatri

626 views

Pooja Khatri asked Mar 19, 2019

0 votes

0 answers

3475

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

268 views

Pooja Khatri asked Apr 4, 2019

0 votes

0 answers

3476

Kenneth Rosen Edition 7 Exercise 2.3 Question 45 (Page No. 154)
Let $f$ be a function from $A$ to $B$. Let $S$ be a subset of $B$. Show that $f^{-1}\sim(S) = \sim f^{-1}(S).$

Let $f$ be a function from $A$ to $B$. Let $S$ be a subset of $B$. Show that $f^{-1}\sim(S) = \sim f^{-1}(S).$

Pooja Khatri

165 views

Pooja Khatri asked Apr 9, 2019

0 votes

0 answers

3477

Kenneth Rosen Edition 7 Exercise 2.2 Question 21 (Page No. 136)
Prove the first associative law from Table 1 by showing that if $A,B,$ and $C$ are sets, then $A \cup (B \cup C)= (A \cup B) \cup C.$

Prove the first associative law from Table 1 by showing that if $A,B,$ and $C$ are sets, then $A \cup (B \cup C)= (A \cup B) \cup C.$

Pooja Khatri

214 views

Pooja Khatri asked Apr 6, 2019

0 votes

0 answers

3478

Kenneth Rosen Edition 7 Exercise 2.3 Question 25 (Page No. 153)
Let $f: R \rightarrow R$ and let $f(x) >0$ for all $x \epsilon R.$ Show that $f(x) $ is strictly decreasing if and only if the function $g(x) = 1/f(x)$ is strictly increasing.

Let $f: R \rightarrow R$ and let $f(x) >0$ for all $x \epsilon R.$ Show that $f(x) $ is strictly decreasing if and only if the function $g(x) = 1/f(x)$ is strictly incre...

Pooja Khatri

185 views

Pooja Khatri asked Apr 9, 2019

1 votes

1 answer

3479

complete lattice and bounded lattice
Prove that every complete lattice is bounded lattice but not vice-versa .

Prove that every complete lattice is bounded lattice but not vice-versa .

Gurdeep Saini

3.2k views

Gurdeep Saini asked Oct 23, 2018

0 votes

0 answers

3480

Kenneth Rosen Edition 7 Exercise 1.5 Question 25 (Page No. 66)
Translate each of these nested quantifications into an English statement that expresses a mathematical fact. The domain in each case consists of all real numbers. $\exists x \forall y (xy=y)$ ... $\forall x \forall y \exists z (x+y =z)$

Translate each of these nested quantifications into an English statement that expresses a mathematical fact. The domain in each case consists of all real numbers.$\exists...

Pooja Khatri

502 views

Pooja Khatri asked Mar 19, 2019

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