Tag: finite and infinite sets

Questions Related to finite and infinite sets

Classify $B = {y | y$ is a factor of $13}$ as 'finite' or 'infinite'.

maths set concepts finite and infinite sets types of sets set language

  1. Infinite

  2. Finite

  3. Data insufficient

  4. None of these

Show answer
Correct Option: B
Explanation:

B is a finite set as 13 has only two factors which are 1, and 13.

The set of fractions between the natural numbers 3 and 4 is a :

maths set concepts finite and infinite sets types of sets set language

  1. Finite set

  2. Null set

  3. Infinite set

  4. Singleton set

Show answer
Correct Option: C
Explanation:

We can have many fractions between the numbers 3 and 4.
Hence, this set is an infinite set

If $A$ is finite set. Let $n(A)$ denote the number of elements in $A$ and $B$ are finite sets, $A\neq B$ and $n(A) = n(B)$. Then $n(A\cap B)$ is

maths set concepts finite and infinite sets types of sets set language

  1.  $ > n(A)$

  2.  $ < n(A)$

  3.  $ \neq n(A)$

  4.  $ \leq n(A)$

Show answer
Correct Option: B

Identify the type of Set
$A= { x| x \epsilon N, 2 \leq x \leq 3}$

maths set concepts finite and infinite sets types of sets set language

  1. Finite Set

  2. Infinite Set

  3. Null Set

  4. Singleton Set

Show answer
Correct Option: A
Explanation:

We have to identify the type of set.

Given $A={x|x\in N, 2 \leq x \leq 3 }$

               $={2,3}$ which is a finite set.

Therefore $A$ is a finite set.

A finite set $S$ is given by $S={x:x\in N: x\le15}.$ Find the cardinality of its power set.

maths set concepts finite and infinite sets types of sets set language

  1. 32952

  2. 16384

  3. 32768

  4. 16476

Show answer
Correct Option: C
Explanation:

$S$ is given by $S={x:x\in N: x\le15}$
$S={1,2,3,4,5,6,7,8,9,10,11,12,13,14,15}$
$\therefore n(S)=15$
The power set is set of all the possible subsets of $S.$
Number of elements in power set $=$ Total number of subsets
So, cardinality of power set $S=2^{15}=32768$

Identify the type of set
$N = {x : x \in  N, x < 7}$ 

maths set concepts finite and infinite sets types of sets set language

  1. Finite Set

  2. Null Set

  3. Infinite Set

  4. Singleton Set

Show answer
Correct Option: A
Explanation:

We have to identify the type of set.


Any set which is empty or contains a definite and countable number of elements is called a finite set. 

Any Set that does not contain any element is called the Null set

For uncountable or indefinite numbers of elements are referred to as  infinite sets.

Singleton Set are those sets that have only a single element.


Given $N=\{x|x\in N, x<7 \}$

               $=\{1,2,3,4,5,6\}$ which has finite number of elements i.e. countable number of elements. So it is a finite set.

Therefore $N$ is a finite set.

Identify the type of set
$B={x: x \epsilon W,x=2n }$ 

maths set concepts finite and infinite sets types of sets set language

  1. Finite Set

  2. Null Set

  3. Infinite Set

  4. Singleton Set

Show answer
Correct Option: C
Explanation:

We have to identify the type of set.

Given $B={x|x\in W, x=2n }$ where $W$ represents a set of whole numbers.

               $={0,2,4,6,8,....}$ which has infinite number of elements. So it is an infinite set.

Therefore $B$ is an infinite set.

Identify the type of set
$A= { x| x \epsilon R, 2 \leq x \leq 3 }$ 

maths set concepts finite and infinite sets types of sets set language

  1. Finite Set

  2. Infinite Set

  3. Null Set

  4. Singleton Set

Show answer
Correct Option: B
Explanation:

We have to identify the type of set.

Given $A={x|x\in R, 2 \leq x \leq 3 }$

$A$ contains all real numbers between $2$ and $3$ which is an infinite set.

Therefore $A$ is an infinite set

Which of the following are countably infinite and uncountably infinte.
$(i)$Set of natural numbers
$(ii)$Set of real numbers

maths set concepts finite and infinite sets types of sets set language

  1. Both $(i)$ and $(ii)$ are uncountably infinite

  2. $(i)$ uncountably infinite and $(ii)$ countably infinite

  3. $(i)$ countably infinite and $(ii)$ uncountably infinite

  4. Both $(i)$ and $(ii)$ are countably infinite

Show answer
Correct Option: C
Explanation:

Countably Infinite: Set of natural numbers are countably infinite because one can count natural number one after other easily.
Uncountably infinite: Set of real numbers are uncountably infinite because real numbers cannot be counted.

State which of the following are infinite sets.
$(i)A={x:x\in Z: x^2 $ is even $}$
$(ii)B={x:x\in R:-4<x<-2}$

maths set concepts finite and infinite sets types of sets set language

  1. $(i)$ only

  2. $(ii)$ only

  3. $(i)$ and $(ii)$ both

  4. Neither $(i)$ nor $(ii)$

Show answer
Correct Option: C
Explanation:

$(i)A={x:x\in Z: x^2 $ is even $}$
$A={...,-6,-4,-2,0,2,4,6,...}$ which is an infinite set.
$(ii)B={x:x\in R:-4<x<-2}$
There will be infinite real numbers any two numbers so, it is an infinite set.