Tag: set concepts

Questions Related to set concepts

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.

If the system of equation $x+2y-3z=1$, $(p+2)z=3$, $(2p+1)y+z=2$ has infinite number of solutions, then the value of p is not equal to.

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

  1. $-2$

  2. $-\displaystyle\frac{1}{2}$

  3. $0$

  4. $2$

Show answer
Correct Option: A
Explanation:
$x+2y-3z=1$
$(p+2)z=3$
$(2p+1)y+z=2$
let $p=5$, $s\in R/ \left\{ -2, 1/2\right\}$
$\therefore z=\dfrac{3}{s+2}$
$\Rightarrow y=\left(2-\dfrac{3}{s+2}\right)\dfrac{1}{(2s+1)}\Rightarrow \dfrac{2s+1}{(s+2)(2s+1)}-\dfrac{1}{s+2}$
$[As\ 2s+1\neq 0]$
$\therefore x=3z+1-2y$
$=\dfrac{9}{s+2}+1-\dfrac{2}{s+2}=\dfrac{7}{s+2}+1$
$\therefore$ solutions $(x, y, z)=\left(\dfrac{7}{s+2}+1, \dfrac{1}{s+2}, \dfrac{3}{s+2}\right)$
is an infinite set,
$\therefore p$ cannot be equal to $-2$ or $1/2$

Let $A = {a, b, c}, B = {a}, C = {a, b}$ then,  which set is the superset of $C$? 

maths set concepts intervals subsets subsets and supersets

  1. Set $A$

  2. Set $B$

  3. Set $A$ and Set $B$

  4. None of these

Show answer
Correct Option: A
Explanation:

$\text{Clearly, set A contain all elements of set C}$
$\Rightarrow \text{A is superset of C}$

If U = {1, 2, 3, .......}; A = {2, 4, 6, 8, .......}; B = {1, 3, 5, .......}, then find (A $\cup$ B)'.

maths set concepts intervals subsets subsets and supersets

  1. A'

  2. B

  3. A

  4. $\phi$

Show answer
Correct Option: D
Explanation:
Given,
$U=(1, 2, 3,....)$
$A=\{2, 4, 6, 8,...\}$
$B=\{1, 3, 5, 7,....\}$

We know,
$(A\cup B)'=U-(A\cup B)$

here
$A\cup B=\{1, 2, 3,....\}=U$

so $(A\cup B)'=\phi$.

The number of subsets with two elements, of the set $S+{1,2,3,4,.....,10}$ such that minimum of the two numbers is less than $6$ is 

maths set concepts intervals subsets subsets and supersets

  1. $35$

  2. $38$

  3. $30$

  4. $40$

Show answer
Correct Option: A

Which of the following sets is a universal set for the other four sets? 

(a) The set of even natural numbers 

(b) The set of odd natural numbers

(c) The set of natural numbers 

(d) The set of negative numbers 

(e) The set of integers 

maths set concepts intervals subsets subsets and supersets

  1. $(e)$

  2. $(a)$

  3. $(b)$

  4. $(c)$

Show answer
Correct Option: A
Explanation:

We know that $\mathbb{N} \subset \mathbb{Z}$ where $\mathbb{N}$ represents set of natural numbers and $\mathbb{Z}$ represents set of all positive and negative integers.

Since $\mathbb{N} \subset \mathbb{Z}$,

                                 $(a),(b),(c)$ are subsets of $(e)$        $...(1)$

Since $\mathbb{Z}$ represents set of all positive and negative integers.

                                      $(d)$ is a subset of $(e)$                   $...(2)$

From $(1)$ and $(2)$ we get

$(a),(b),(c),(d)$ are subsets of $(e)$.

Hence $(e)$ is the universal set for the other four sets.