Question

if A = { x : x = 4 + 1 , 2 < n < 5 } then the number of subsets of A

Answer 1

The question is seemed as error, hence question is edited and given below:

"If $A=\{x: x=4n+1,\ n\in \mathbb{N},\ 2<n<5\},$ then find the no. of all subsets of A."

First we have to find out the possible values of x.

$n\in \mathbb{N}\ \wedge\ 2<n<5\ \ \ \ \ \Longrightarrow\ \ \ \ \ n\in \{3,\ 4\}$

Let n = 3.

4n + 1 = 4 • 3 + 1 = 12 + 1 = 13.

Let n = 4.

4n + 1 = 4 • 4 + 1 = 16 + 1 = 17.

$A=\{13,\ 17\}$

All subsets of a set are included in the power set of that set, conversely, the power set of a set contains all subsets of that set.

The cardinality of the power set of a set S having 'n' no. of elements, means |S| = n, is 2^n.

Here,

|A| = 2.

$\therefore\ \mid P(A)\mid\ = 2^2=\mathbf{4}$

Hence set A has a total of 4 subsets.

$P(A)=\{\{\},\ \{13\},\ \{17\},\ \{13,\ 17\}\}$

Answer 2

ANSWER:

"If then find the no. of all subsets of A."

First we have to find out the possible values of x.

Let n = 3.

4n + 1 = 4 • 3 + 1 = 12 + 1 = 13.

Let n = 4.

4n + 1 = 4 • 4 + 1 = 16 +1=17