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

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?

  1. Finite sets

  2. Infinite sets

  3. Cannot be determined

  4. None of these
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

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

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

The set of all animals on the earth is a 

  1. Finite set

  2. Singleton set

  3. Null set

  4. Infinite set
Reveal answer Fill a bubble to check yourself
A Correct answer
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.

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

Which of the following sets is non - empty ?

  1. Set of odd natural numbers divisible by 2
  2. ${x: x+4=0, x\in N}$

  3. Set of even prime numbers
  4. ${x:2< x< 3,x\in N}$
Reveal answer Fill a bubble to check yourself
C Correct answer
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 $

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

Which one of the following sets is infinite?

  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
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

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

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

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

  1. $(A\cup B)\cup (B\cap C)$
  2. $(A\cap B)\cup (A\cap C)$
  3. $A\cup (B\cap C)$
  4. $(A\cup B)\cap (B\cup C)$
Reveal answer Fill a bubble to check yourself
B Correct answer
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.

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

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

  1. True

  2. False
Reveal answer Fill a bubble to check yourself
A Correct answer
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.

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

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.

  1. $(i)$ only
  2. $(i),(ii)$ and $(iii)$
  3. $(i)$ and $(ii)$
  4. $(ii)$ and $(iii)$
Reveal answer Fill a bubble to check yourself
A Correct answer
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.