Subsets...!?!

Algebra Level 4

A,B,C are finite sets.A has twice as many elements as B.B has more elements than C.the number of subsets of B is 15more than that of C.then the number by which the number of subsets of A exceeds the number of subsets of B is n .Find n.

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The answer is 240.

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1 solution

Palash Som
May 17, 2015

THE solution is too simple see The subsets of B \boxed{B} are 15 more than that in C \boxed{C} The number of subsets of a set is given by the formula - 2 n 2^n where n \boxed{n} is the number of elements in a set So 2 n 2^n must always be even , even after subtraction from any power of 2 But here it is positive which clearly states that C \boxed{C} has only 1 subset so the set C \boxed{C} is a null set you can compare 2 x 2^x - 2 0 2^0 = 15 and solve for the value of x \boxed{x} which would come out to be 4 since set A \boxed{A} has twice the elements of set B \boxed{B} therefore you can apply the similar formula of 2 n 2^n to the set A \boxed{A} and subtract it from the subsets in B \boxed{B} AND ANSWER WILL BE 240 \boxed{240}

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