Question

The cardinal number of A = {x/x € N ; x = 4n^2 + 5n + 10/n,Where n€N}​

Answer 1

Answer:

The cardinal number of the set A = 4

Step-by-step explanation:

Given,

A =  {x/x € N ; x = $4n^2 + 5n + \frac{10}{n}$, Where n€N}​

To find,

The cardinal number of the set A

Recall the concept

The cardinal number of a set is defined as the number of elements in the set

Solution:

Since given set is  A = {x/x € N ; x = $4n^2 + 5n + \frac{10}{n}$, Where n€N}​,

The elements of the set A are the values of x such that

x = $4n^2 + 5n + \frac{10}{n}$ and also x is a natural number

x is a natural number ⇒ $4n^2 + 5n + \frac{10}{n}$ is a natural number

⇒ $\frac{10}{n}$ is a natural number, (since 4n² +5n is always a natural number for all values of n)

$\frac{10}{n}$ is a natural number if 10 is divisible by n

that is, 10 is divisible by n if the values of n = 1,2,5,10

Corresponding the values of n =1,2,5,10, x has 4 values

Hence set A contains 4 elements

The cardinal number of the set A = 4

#SPJ2