Register

TIFR-2016-Maths-A: 12

• edited by
150 views
0 votes
0 votes

Let $A$ be a subset of $\left [ 0,1 \right ]$ with non-empty interior, and let  $\mathbb{Q}+A=\left \{ q+a:q\in\mathbb{Q},a\in A \right \}$. Which of the following is true ?

  1. $\mathbb{Q}+A=\mathbb{R}$
  2. $\mathbb{Q}+A$ can be a proper subset of  $\mathbb{R}$
  3. $\mathbb{Q}+A$ need not be closed is $\mathbb{R}$
  4. $\mathbb{Q}+A$ need not be open in $\mathbb{R}$.
• edited by
User Avatar

Please log in or register to answer this question.

Voting & Accepting an answer helps improve the community
Answer:
← PreviousNext →
← Previous in categoryNext in category →

Related questions

0 votes
0 votes
0 answers
1
soujanyareddy13 asked Aug 30, 2020
259 views
TIFR-2016-Maths-A: 1
The value of the product $\left ( 1+\frac{1}{1!} +\frac{1}{2!}+\cdots \right )\left ( 1-\frac{1}{1!} +\frac{1}{2!}-\frac{1}{3!}+\cdots \right )$ is $1$ $e^{2}$ $0$ $log_{e} \:2$.
The value of the product $\left ( 1+\frac{1}{1!} +\frac{1}{2!}+\cdots \right )\left ( 1-\frac{1}{1!} +\frac{1}{2!}-\frac{1}{3!}+\cdots \right )$ is $1$$e^{2}$$0$$log_{e} ...
User Avatar
0 votes
0 votes
0 answers
2
soujanyareddy13 asked Aug 30, 2020
176 views
TIFR-2016-Maths-A: 3
The value of the series $\sum _{n=1}^{\infty }\frac{n}{2^{n}}$ is $1$ $2$ $3$ $4$.
The value of the series $\sum _{n=1}^{\infty }\frac{n}{2^{n}}$ is$1$$2$$3$$4$.
User Avatar
0 votes
0 votes
0 answers
3
soujanyareddy13 asked Aug 30, 2020
170 views
TIFR-2016-Maths-A: 5
Which of the following continuous functions $f:\left ( 0,\infty \right ) \rightarrow \mathbb{R}$ can be extended to a continuous function on $\left [ 0,\infty \right )$ ? $f\left ( x \right )=sin\frac{1}{x}$ $f\left ( x \right )=\frac{1-cos\:x}{x^{2}}$ $f\left ( x \right )=cos\frac{1}{x}$ $f\left ( x \right )=\frac{1}{x}$
Which of the following continuous functions $f:\left ( 0,\infty \right ) \rightarrow \mathbb{R}$ can be extended to a continuous function on $\left [ 0,\infty \right )$ ?...
User Avatar
Link Copied!