Question

Find the number of subsets and the number of proper subsets of the following sets.
(1) A = {13, 14, 15, 16, 17, 18}
(ii) B = {a,b,c,d,e.f,g}
3.
(i)
If A = Ø, find n[P(A)]
(ii) If n(A) = 3, find n[P(A)]
If n[P(A)]= 512 find n(A)
5.
If n[P(A)] = 1024 find n(A)​

Answer 1

Step-by-step explanation:

(1) A = { 13,14,15,16,17,18}

=> number of elements of A = 6

=> number of subsets of A = 2^6 = 64

B= {a,b,c,d,e,f,g}

=> number of elements of B = 7

=> number of subsets of B = 2^7 = 128

(3) (I)A = fi. => P(A) ={fi} => n(P(A)) = 2^0 = 1

(ii) n(A) = 3=> n[P(A)] = 2³= 8

(4) if n[P(A)] = 512 = 2^9 => n(A) = 9

(5) if n[P(A)] = 1024 = 2^10 => n(A) = 10

formula used

if number of elements of a set A = n

=> number of sunsets of A= 2ⁿ

if n(A) = n => n[P(A) = 2ⁿ

hope this helps you

Answer 2

Given:

Sets of number

To Find:

The number of subsets and the number of proper subsets of the given sets.

Solution:

Using, if the number of elements of set A =n

Number of subsets of A = $2^{n}$

(1) A = {13, 14, 15, 16, 17, 18}

In the A set number of elements = 6

So, number of subsets = $2^{6}$

                                      = 64

(2) B = {a, b, c, d, e, f, g}

   Number of subsets of B

       =  $2^{7}$

       = 128

(3) A = ∅, then

n[P(A)] = $2^{0}$

          = 1

(4) Now, n[P(A)] = 125 then

n(A) = 2³

      = 8

(5) n[P(A)] = 1024 then

n(A) = $2^{10}$

      = 10