Tag: maths

Questions Related to maths

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

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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

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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 $(iii)$

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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} $

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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.

Which of the following is incorrect.

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

  1. The power set of an infinite set is infinite.

  2. The union of two infinite set is infinite.

  3. The intersection of two infinite set is infinite.

  4. The cardinality of an infinite set is infinite.

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Correct Option: C
Explanation:

The intersection of an infinite set may be finite.
Example:
$A={x:x\in N; x>2}$
$B={x:x\in I; x<5}$
Here, Both $A$ and $B$ are infinite but its intersection are finite.

Define infinite set .
Is ${x:x\in R:1\le x\le 3}$ a infinite set?

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

  1. True

  2. False

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Correct Option: A
Explanation:

Definition: A set having infinite number of elements is known as infinite set.
 ${x:x\in R:1\le x\le 3}$ is a infinite set because since $x\in R$, there are infinte number of real numbers lie in between two numbers.

Choose that set of numbers from the option set that is similar to the given set {10,15,65}

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

  1. ${10, 6, 5}$

  2. ${124, 5, 3}$

  3. ${95, 25, 5}$

  4. ${168, 15, 4}$

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Correct Option: C
Explanation:

option C 

since in both the given set all the elements are divisible y 5 

Let S be the set of all values of x such that $log _{2x}(x^{2}+5x+6)<1$ then the sum of all integral value of x in the set S, is

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

  1. 0

  2. 8

  3. 9

  4. 10

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Correct Option: A
Explanation:
$ log _{2x}(x^{2}+5x+6)< 1 $

$ \Rightarrow x^{2}+5x+6< 2x^1 $

$ \Rightarrow x^{2}+3x+6< 0 $

But $ x^{2}+3x+6 = 0 $ has no real roots 

$ \therefore S$  is an empty set 

$ \therefore $ sum of all integral values of $ x = 0 $ 

If a set contains $n$ elements then number of elements in its power set is

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

  1. $2^n-n$

  2. $2^n-2$

  3. $2^n$

  4. $n^2$

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Correct Option: C
Explanation:

Given the set contains $n$ elements.

Then its power set will contains $2^n$ elements.