Q1 of 5 Page 24

If n[p(a)] = 64, then n(a)=?

Formula:- if am = an, then m = n.


N(A) = Number of elements in set A


P(A) = Power Set of A = Set of all the sets possible by the elements of A.


For Example, Let A = {1, 2, 3}


Then, P(A) = {Ø, (1), (2), (3), (1, 2), (2, 3), (3, 1), (1, 2, 3)}


So there are 8 sets in the power set of A.


We know that n[P(A)] = Number of elements in the power set of A.


If n is the number of elements in A, the number of elements in the power set of A = 2n


Given: n[p(a)] = 64


Let the number of elements in set A = x


Then, n(p(a)) = 2x


Therefore, 2x = 64


2x = 26


x = 6


Hence, n(a) = 6


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