Intervals as Subsets of Real Numbers

Q. Which of the following represent the collection of all the real numbers on a number line?

1. $(-\infty ,\infty ]$
2. $(-\infty ,\infty )$
3. $[-\infty ,\infty ]$
4. $[-\infty ,\infty )$

Q. The correct representation of the set of all real numbers greater than or equal to 2 is given by

1. $(2,\infty )$
2. $(2,\infty ]$
3. $[2,\infty )$
4. $[2,\infty ]$

Q. For the given intervals of integers, match the following intervals by it's length.

1. $4$
2. $14$
3. $10$
4. $8$

Q. The set $\{y:y\in R,2\le y<8\}$ can be written in interval as

1. $[2,8)$
2. $[2,8]$
3. $(2,8]$
4. $(2,8)$

Q. Choose the correct Set-builder representation of the interval $[-5,9)$.

1. $\{p:p\in R,-5\le p\le 9\}$
2. $\{p:p\in R,-5\le p<9\}$
3. $\{p:p\in R,-5<p\le 9\}$
4. $\{p:p\in R,-5<p<9\}$

Q. Length of the interval $(-3,-2)$ is

1. $5$
2. $-1$
3. $1$
4. $-5$

Q. If $A=\{x\in R:|x|<2\}$ and $B=\{x\in R:|x-2|\ge 3\},$ then

1. $A\cap B=(-2,-1)$
2. $B-A=R-(-2,5)$
3. $A-B=[-1,2)$
4. $A\cup B=R-(2,5)$

Q. If $A=\{x\in R:|x|<2\}$ and $B=\{x\in R:|x-2|\ge 3\},$ then

1. $A\cap B=(-2,-1)$
2. $B-A=R-(-2,5)$
3. $A-B=[-1,2)$
4. $A\cup B=R-(2,5)$

Q. Which of the following intervals are subsets of the interval $[-3,7)$

1. $(3,7)$
2. $(-1,7]$
3. $(-1,7)$
4. $(-3,-1)$