Question

.If A is a set of first 10 natural numbers then number of subsets of A are *
answer
1024
correct​

Answer 1

$\underline{\textsf{Given:}}$

$\textsf{Set A has 10 elements}$

$\underline{\textsf{To find:}}$

$\textsf{Number of subsets of A}$

$\underline{\textsf{Solution:}}$

$\underline\mathsf{Concept\;used:}$

$\mathsf{If\;A\;has\;m\;elements,\;then\;number\;of\;subsets\;of\;A\;is\;2^m}$

$\boxed{\mathsf{If\;n(A)=m,\;then\;n[P(A)]=2^m}}$

$\mathsf{Here,\;n(A)=10}$

$\mathsf{Then,\;number\;of\;subsets\;of\;A}$

$\mathsf{=2^{n(A)}}$

$\mathsf{=2^{10}}$

$\mathsf{=1024}$

$\therefore\mathsf{Number\;of\;subsets\;of\;A\;is\;1024}$

$\underrline{\textsf{Find more:}}$

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Answer 2

Given :- .If A is a set of first 10 natural numbers then number of subsets of A are ?

Solution :-

we know that,

• If a set contains ‘n’ elements, then the number of subsets of the set is 2^n .
• Example :- If A = {p, q} the total subsets of A are [{ }, {p}, {q},{p,q}] = 2² = 4 .

So,

→ A = first 10 natural numbers = [1,2,3,4,5,6,7,8,9,10].

then,

→ Total subsets of A = 2¹⁰ = 1024 (Ans.)

Hence, number of subsets of A are 1024.

{ If a set contains ‘n’ elements, then the number of proper subsets of the set are (2^n - 1). }

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