Find the number of proper subsets of the set X-x2- x - N- x2- 100A- 511B- 1024C- 1023D- 512

The correct option is C 1023Given, nbsp; X = { x^2 : x ∈ N, x2 ≤ 100} X = {1, 4, 9, 16, 25, 36, 49, 64, 81, 100} The number of elements in set X, n(X) = 10 ...

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Standard IX

Mathematics

Subset

Find the numb...

Question

Find the number of proper subsets of the set
$X = {x^{2} : x ϵ N, x^{2} \leq 100}$

512

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511

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1024

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1023

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Solution

The correct option is D 1023
Given,
$X = {x^{2} : x \in N, x 2 \leq 100}$
$X = {1, 4, 9, 16, 25, 36, 49, 64, 81, 100}$

The number of elements in set X,
$n (X) = 10$

The Number of subsets
$= n [P (X)]$
$= 2^{10}$
$= 1024$

The Number of proper subsets
$= n [P (X)] - 1$
$= 2^{10} - 1$
$= 1024 - 1$
$= 1023$

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Find the number of proper subsets of the set X={x2:x ϵ N,x2≤100}

The correct option is D 1023Given, X={x2:x∈N,x2≤100} X={1,4,9,16,25,36,49,64,81,100} The number of elements in set X, n(X)=10 The Number of subsets =n[P(X)] =210 =1024 The Number of proper subsets =n[P(X)]–1 =210–1 =1024–1 =1023

Find the number of proper subsets of the set
$X = {x^{2} : x ϵ N, x^{2} \leq 100}$