Tag: set language

Quizzes (7) Questions (71)

Questions Related to set language

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

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

  1. $ > n(A)$
  2. $ < n(A)$
  3. $ \neq n(A)$
  4. $ \leq n(A)$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

If A and B are finite sets with the same number of elements (n(A) = n(B)) but A is not equal to B, then the intersection A intersect B must contain fewer elements than A. If it contained n(A) elements, then A would have to be a subset of B, and since they have the same size, A would equal B.

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

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

  1. Finite Set

  2. Infinite Set

  3. Null Set

  4. Singleton Set
Reveal answer Fill a bubble to check yourself
A Correct answer
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.

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

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

  1. 32952

  2. 16384

  3. 32768

  4. 16476
Reveal answer Fill a bubble to check yourself
C Correct answer
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 $S=2^{15}=32768$

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

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

  1. Finite Set

  2. Null Set

  3. Infinite Set

  4. Singleton Set
Reveal answer Fill a bubble to check yourself
A Correct answer
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.
Multiple choice maths set concepts finite and infinite sets types of sets set language

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

  1. Finite Set

  2. Null Set

  3. Infinite Set

  4. Singleton Set
Reveal answer Fill a bubble to check yourself
C Correct answer
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.

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

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

  1. Finite Set

  2. Infinite Set

  3. Null Set

  4. Singleton Set
Reveal answer Fill a bubble to check yourself
B Correct answer
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

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

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

  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
Reveal answer Fill a bubble to check yourself
C Correct answer
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.