8. Find the number of subsets and the number of proper subsets of the following sets.
(i) W = {red, blue, yellow} (ii) X = { x2 : x ∈N, x2 ≤ 100}.
Answers
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
Answer:
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
Step-by-step explanation:
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