Set Builder Form

Q.

Write the cardinal number for the set $A=\left\{x:xisaletterinthewordIMPORTANT\right\}$.

Q. A set $Y$ is set of all integers $k$ greater than $-10$ and less than $5$ can be represented as:

1. $Y=\{-10,-9,-8,...,3,4,5\}$
2. $Y=\{-9,-8,-7,-6,...,2,3,4\}$
3. $Y=\{k:k>-10\&k<5\&k\in I\}$
4. $Y=\{k:k<-10\&k>5\&k\in I\}$

Q. The set $X=\{5,10,15,20,25\}$ can be written in Set-builder form as:

1. $X=\{y:y=5a,a\in N,a<5\}$
2. $X=\{y:y=5a,a\in N,a\le 5\}$
3. $X=\{y:y=5a,a\in N,a\le 6\}$

Q. Let $A=\{x:2<|x|\le 5\text{and}x\in Z\}$ and $B$ be the set of values of $a$ for which the equation $||x-1|+a|=4$ can have real solutions. Then $n(A\cap B)$ is

1. $0$
2. $1$
3. $2$
4. $5$

Q. The set builder form of $\{\frac{1}{2},\frac{2}{3},\frac{3}{4},\frac{4}{5},\frac{5}{6}\}$ is

1. $\{x:x=\frac{n}{n+1}$, where $n$ is a natural number and $1\le n\le 6\}$
2. $\{x:x=\frac{n}{n+1}$, where $n$ is a natural number and $1\le n\le 5\}$
3. $\{x:x=\frac{n}{n+1}$, where $n$ is a natural number and $2\le n\le 6\}$
4. $\{x:x=\frac{n}{n-1}$, where $n$ is a natural number and $1\le n\le 5\}$

Q. A set $A=\{b:b<5\&b\in I\}$, where $I$ denote integers, then tap on the correct bubbles.

1. $5\in A$
2. $6\in A$
3. $-6\in A$
4. $0\in A$
5. $3\in A$
6. $-336\in A$
7. $500\in A$
8. $-10\in A$
9. $-3\in A$

Q. The most appropriate option for the following sets
$A$ is set of letters of the word 'debit card'
$B$ is the set of letters of the word 'bad credit'

1. $A$ and $B$ are equivalent sets
2. $A$ and $B$ are unequal sets
3. $A$ and $B$ are similar sets
4. $A$ and $B$ are identical sets

Q. A set $Y$ containing all elements $x$ such that $x$ is a whole number less than $10$ can be represented in Set-builder form as:

1. $Y=\{x:x<11\&x\in W\}$
2. $Y=\{x:x<10\&x\in W\}$
3. $Y=\{x:x>10\&x\in W\}$