Question

Write the cardinal number of the set of all integers x for which 30/x is a natural number.​

Answer 1

30 => 2 × 5× 3

factors of 30 are 2,5,3,10,15,6,30,1

for 30/x to be natural

x should be any factor for 30/x to be natural

So x values are 1,2,3,5,6,10,15,30

Answer 2

Concept:

The Cardinal Number of the set can be defined as the number which is present in that set.

Given:

A natural number 30/x

Find:

The Cardinal numbers of the set which contain all integers x for which 30/x is a natural number.

Solution:

Let, the set of the numbers be S.

Let, S ={x / x ∈ Z, and 30/x ∈ N}

So, the numbers are 1, 2, 3, 5, 6, 10, 15, 30.

S={1, 2, 3, 5, 6, 10, 15, 30}

So, n(S) = 8.

Hence, the cardinal number of the set of all integers x for which 30/x is a natural number is {1, 2, 3, 5, 6, 10, 15, 30} and the number of elements in the set is 8.

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