The set A - - x-x-n-1-n- -where- n-N - is -a finite seta null setan infinite setsingleton set

The correct option is C an infinite setGiven, A = { x:x=n 1/n, where n ϵ N } Substituting n = 1, 2, 3,........ we get, A = { 0, 1/2, 2/3……} Set A has infinit ...

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Standard IX

Mathematics

Finite and Infinite Sets

The set A = {...

Question

The set $A = {x : x = \frac{n - 1}{n}, where n ϵ N}$ is __________.

a finite set

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a null set

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an infinite set

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singleton set

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Solution

The correct option is C an infinite set
Given, $A = {x : x = \frac{n - 1}{n}, where n ϵ N}$

Substituting n = 1, 2, 3,........ we get,

$A = {0, \frac{1}{2}, \frac{2}{3} \dots \dots}$

Set A has infinite number of elements therefore, A is an infinite set.

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Similar questions

State whether each of the following sets is a finite set or an infinite set:

(i) The set of multiples of 8.

(ii) The set of integers less than 10.

(iii) The set of whole numbers less than 12.

(iv) ${x : x = 3 n - 2, n \in W, n \leq 8}$ (v) ${x : x = 3 n - 2, n \in Z, n \leq 8}$ (vi) ${x : x = \frac{n - 2}{n + 1}, n \in W}$

Q. The set

A = {x : x = \frac{n - 1}{n}, where n ϵ N}

is __________.

Q. The set

B = {x : x = 3 n + 1, n ϵ N and n \leq 20}

is _________.

Q. The set

A = {x : x = \frac{n - 1}{n}, where n ϵ N}

is __________.

Q. State, whether each of the following sets is a finite set or an infinite set:

{x : x = \frac{n - 2}{n + 1}, n \in W}

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The set A={x:x=n−1n, where n ϵ N} is __________.

The correct option is C an infinite setGiven, A={x:x=n−1n, where n ϵ N} Substituting n = 1, 2, 3,........ we get, A={0,12,23……} Set A has infinite number of elements therefore, A is an infinite set.

The set $A = {x : x = \frac{n - 1}{n}, where n ϵ N}$ is __________.

The correct option is C an infinite set
Given, $A = {x : x = \frac{n - 1}{n}, where n ϵ N}$

Substituting n = 1, 2, 3,........ we get,

$A = {0, \frac{1}{2}, \frac{2}{3} \dots \dots}$

Set A has infinite number of elements therefore, A is an infinite set.