Question

If A = { x: x is a factor of 15), then n(A) is​

Answer 1

If A = { x : x is a factor of 15 } then n(A) = 4

Given :

The set A = { x : x is a factor of 15 }

To find :

The value of n(A)

Solution :

Step 1 of 2 :

Write down the given set

Here the given set A = { x : x is a factor of 15 }

Step 2 of 2 :

Find the value of n(A)

On prime factorisation of 15 we get

15 = 3 × 5

So the factors of 15 are 1 , 3 , 5 , 15

Thus we get

A

= { x : x is a factor of 15 }

= { 1 , 3 , 5 , 15 }

∴ n(A)

= Number of elements in A

= 4

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Answer 2

We need to recall the following definitions.

• Factor: The factor of a number is a number that divides the given number.
• Cardinality of a set: Cardinality of a set is a number of unique elements present in a set.

Given:

$A= \{x:x$ is a factor of $15\}$

Factors of $15$ are: $1$ , $3$ , $5$ , $15$

Thus, we get

$A=\{1,3,5,15\}$

Hence, the cardinality of the set is,

$n(A)=4$