Finite Set

Q.

List the elements of sets of first three even natural numbers $?$

Q. The correct options among the following is/are

1. If $A=\{x:x\text{is a prime number less than}2\}$, then $A$ is a singleton set
2. If $B=\{x:x\in Z\text{and}|x-2|\le 5\}$, then $B$ is a finite set
3. If $C=\{x:x\in Z\text{and}|x|<0\}$, then $C$ is a null set
4. If $D=\{x:x\text{is a natural number greater than}100\}$, then $D$ is an infinite set

Q.

Classify the set of multiples of $9$ more than $8$ and less than $46$as finite and infinite set.

Q.

Which of the following are singleton sets?

$\left\{Mountainpeaksmorethan6000mhigh\right\}$

Q.

State whether the given set is finite or infinite.

$\left\{x:x\text{is a prime number}\right\}$

Q.

Identify the finite and infinite sets and find the cardinal numbers of the finite sets$.$

$A=\{x:x>4$and $x\in N\}$

Q. A Set $X=\{y:-2<y\le 10,y\in I\},$ then the set $X$ is a

1. Null set
2. Finite Set

Q. Let $f,g:N\to N$ such that $f(n+1)=f\left(n\right)+f\left(1\right),\forall n\in N$ and $g$ be any arbitrary function. Which of the following statements is $\text{NOT}$ true $?$

1. If $g$ is onto, then $fog$ is one-one
2. If $f$ is onto, then $f\left(n\right)=n\forall n\in N$
3. $f$ is one -one
4. If $fog$ is one-one, then $g$ is one-one

Q.

State whether the given set is finite or infinite.

$\left\{x:x\text{is a prime number less than 10}\right\}$

Q. The number of elements in the power set of the set $\left\{\right(a,b):a^2+b^2=7,a,b\in Z\}$ is

1. $2$
2. $1$
3. $4$
4. $6$