Tag: maths

Questions Related to maths

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.

Which of the following are infinite set?
$(i)$The set of lines which are parallel to x-axis.
$(ii)$The set of animals living on the earth.
$(iii)$ The set of numbers which are multiple of $5.$
$(iv)$ The set of the circles passing through the origin $(0,0).$

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

  1. $(i),(ii)$ and $(iv)$

  2. $(ii)$ only

  3. $(i),(iii)$ and $(iv)$

  4. $(i),(ii)$ and $(iii)$$

Show answer
Correct Option: C
Explanation:

$(i)$The set of lines which are parallel to x-axis is an infinite set because line parallel to x-axis are infinite in number.
$(ii)$The set of animals living on the earth is a finite set because the number of animals living on the earth is finite (although it is quite a big number)
$(iii)$ The set of numbers which are multiple of $5$ is an infinite numbers multiples of $5$ are infinite in number.
$(iv)$ The set of the circles passing through the origin $(0,0)$ is an infinite set because infinite number of circles can pass through the origin.

Which of the following sets are finite sets.
$(i)$ The sets of months in a year.
$(ii){1,2,3,....}$
$(iii){1,2,3,...,99,100}$
$(iv)$ The set of positive integers greater than $100.$ 

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

  1. $(i)$ and $(iii)$

  2. $(i)$ only

  3. $(ii),(iii)$ and $(iv)$

  4. $(ii)$ and $(iv)$

Show answer
Correct Option: A
Explanation:

$(i)$ The sets of months in a year is a finite set because it has $12$ elements.
$(ii){1,2,3,....}$ is an infinite set as it has infinite number of elements.
$(iii){1,2,3,...,99,100}$ is a finite set as it has number from $1$ to $100$ which is finite in number.
$(iv)$ The set of positive integers greater than $100$ is an infinite set because positive integers greater than $100$ are infinite in number. 

If $A={a,{b}},$ find $P(A).$

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

  1. $P(A)={\phi,a,{b},{a,{b}}}$

  2. $P(A)={a,{b},{a,{b}}}$

  3. $P(A)={\phi,{a,{b}}}$

  4. $P(A)={{a,{b}}}$

Show answer
Correct Option: A
Explanation:

Given that:
$A={a,{b}},$
 $P(A)={\phi,a,{b},{a,{b}}}$

State which of the following are infinite sets.
$(i)A={x:x\in Z: x $ is odd$}$
$(ii)B={x:x\in R:<-10}$

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 $}$
$A={...,-3,-1-1,3,...}$ which is an infinite set.
$(ii)B={x:x\in R:-2<x<-4}$
$B={...,-14,-13,-12,-11}$ so it is an infinite set.

State whether the following statement is True or False
$A= { x| x\ is\ a\ negative\ integer\ ;x>-5 }$ is a finite set.

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

  1. True

  2. False

Show answer
Correct Option: A
Explanation:

We have to state whether the statement "$A={x|x:is:a:negative:integer:;x>-5} : is:a:finite : set$" is true or false.

Consider $A={x|x:is:a:negative:integer:;x>-5} $
                     $={-4,-3,-2,-1} $ which has finite number of elements.

So $A$ is a finite set.

Hence the given statement is true.