Tag: set concepts

Questions Related to set concepts

Let $G = {x | x$ is boy of your class$}$ and $H = {y | y$ is a girl of your class$}$. What type of sets G and H are?

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

  1. Finite sets

  2. Infinite sets

  3. Cannot be determined

  4. None of these

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Correct Option: A
Explanation:

Since the number of boys and girls in a class are always finite.
Therefore, set G and H are finite sets.

Classify $C = {..., -3, -2, -1, 0}$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

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Correct Option: A
Explanation:

C is an infinite set as there are many numbers less than $ - 3 $

The set of all animals on the earth is a 

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

  1. Finite set

  2. Singleton set

  3. Null set

  4. Infinite set

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Correct Option: A
Explanation:

Since the numbers of animals on the earth are countable(limited).
Therefore, set of all the animals on the earth is "finite" set.
Option A is correct.

Which of the following sets is non - empty ?

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

  1. Set of odd natural numbers divisible by 2

  2. ${x: x+4=0, x\in N}$

  3. Set of even prime numbers

  4. ${x:2< x< 3,x\in N}$

Show answer
Correct Option: C
Explanation:

A non empty set has atleast one element.

From the given options we see that the SET C has one element which is $ 2 $

Which one of the following sets is infinite?

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

  1. Set of all integers greater than $5$

  2. Set ofall integers between $-10^{10}$ and $+10^{10}$

  3. Set of all prime numbers between $0$ and $10^{100}$

  4. Set of all even prime numbers

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Correct Option: A
Explanation:

(2), (3), and (4) are finite sets.

The set of positive integers is ..................

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

  1. Infinite

  2. Finite

  3. Subset

  4. Empty

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Correct Option: A
Explanation:

The set of positive integers is never ending. There is no such defined largest integer. Hence the set is infinite

For any three sets A, B and C, $A \cap (B \cup C)$ is

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

  1. $(A\cup B)\cup (B\cap C)$

  2. $(A\cap B)\cup (A\cap C)$

  3. $A\cup (B\cap C)$

  4. $(A\cup B)\cap (B\cup C)$

Show answer
Correct Option: B
Explanation:

In the problem statement we are taking union of $B$ and $C$ and then taking its intersection with $A$.

This means $A\cap (B\cup C)$will contain elements that are in $A$ and are in either $B$ or $C$.
$\therefore A\cap (B\cup C) $ is equivalent to taking intersection of $A,B$ and $A,C$ and then taking there union i.e. $(A\cap B)\cup(A\cap C)$
Hence, option B is correct.

Define finite set.
Is $A=$set of animals on the earth 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:

Definition: A finite set is a set which has fixed or finite number of elements.
$A=$ Set of animals on the earth is a finite set because number of animals on the earth is large in number, but it is finite/fixed.

State which of the following are finite sets.
$(i){x:x\in N }$ and $(x-1)(x-2)=0.$
$(ii){x:x\in N }$ and $x$ is prime.
$(ii){x:x\in N }$ and $x$ is odd.

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

  1. $(i)$ only

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

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

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

Show answer
Correct Option: A
Explanation:

$(i)(x-1)(x-2)=0$

$\Rightarrow x-1=0$ or $x-2=0$
$\Rightarrow x=1$ or $x=2$, Number of solutions of equation are finite.
$(ii){2,3,5,7,11,...}$, This set contains infinte number of elements.
$(iii){..,1,3,5,7,...}$, This set contains infinite number of elements. 

Which of the following sets is not a finite set ?

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

  1. ${ (x,y):{ x }^{ 2 }+{ y }^{ 2 }\le 1\le x+y,\ \ x,y\in R} $

  2. ${ (x,y):{ x }^{ 2 }+{ y }^{ 2 }\le 1\le x+y,\ \ x,y\in Z} $

  3. ${ (x,y):{ x }^{ 2 }\le y\le |x|,\ \ x,y\in Z} $

  4. ${ (x,y):{ x }^{ 2 }+{ y }^{ 2 }=1,\ \ x,y\in Z} $

Show answer
Correct Option: A
Explanation:

The set ${ (x,y):{ x }^{ 2 }+{ y }^{ 2 }\le 1\le x+y,\ \ x,y\in R} $ consists of all the points in the first quadrant which lie inside the circle ${ x }^{ 2 }+{ y }^{ 2 }=1$ and above the line $x+y=1$ .So, it is not a finite set.
Option $A$ is correct.