Question

I) w={red,blue,yellow}
ii) x= {x^2:x€ n,x^2 <10} .find the number of subsets and the number of proper subsets of the following.

Answer 1

Step-by-step explanation:

We know that

If a set contains n elements, then the number of subsets of the set is 2ⁿ

And

If a set contains n elements, then the number of proper subsets of the set is 2ⁿ - 1

So, we have

1) W = {red, blue, yellow} we have n = 3

No. of subsets of W = 2³ = 8

No. of proper subsets of W = 2³ - 1 = 7

Subsets of W are =

{ }, {red}, {blue}, {yellow}, {red, blue}, {red, yellow}, {blue, yellow}, {red, blue, yellow}

And proper subsets are all same except the last one i.e. {red, blue, yellow}

2) X = { x² : x ∈ N, x² ≤ 100}

X = {1, 4, 9, 16, 25, 36, 49, 64, 81, 100} here n = 10

No. of subsets of X = 2¹⁰ = 1024

No. of proper subsets of X = 2¹⁰ - 1 = 1023