A,B,C are three sets such that n(A)=2,n(B)=3,n(C)=4, If P(x) denotes power set of X,
K=n(P(P(C)))/n(P(P(A)))*n(P(P(B))). Sum of digits of K is 

Asked by Anil | 20th May, 2017, 10:36: PM

Expert Answer:

begin mathsize 16px style straight n left parenthesis straight A right parenthesis equals 2 rightwards double arrow straight P left parenthesis straight A right parenthesis equals 2 squared equals 4 rightwards double arrow straight P left parenthesis straight P left parenthesis straight A right parenthesis right parenthesis equals 2 to the power of 4
straight n left parenthesis straight B right parenthesis equals 3 rightwards double arrow straight P left parenthesis straight B right parenthesis equals 2 cubed equals 8 rightwards double arrow straight P left parenthesis straight P left parenthesis straight B right parenthesis right parenthesis equals 2 to the power of 8
straight n left parenthesis straight C right parenthesis equals 4 rightwards double arrow straight P left parenthesis straight C right parenthesis equals 2 to the power of 4 equals 16 rightwards double arrow straight P left parenthesis straight P left parenthesis straight C right parenthesis right parenthesis equals 2 to the power of 16

straight K equals fraction numerator straight n left parenthesis straight P left parenthesis straight P left parenthesis straight C right parenthesis right parenthesis right parenthesis over denominator straight n left parenthesis straight P left parenthesis straight P left parenthesis straight A right parenthesis right parenthesis right parenthesis cross times straight n left parenthesis straight P left parenthesis straight P left parenthesis straight B right parenthesis right parenthesis right parenthesis end fraction
straight K equals fraction numerator 2 to the power of 16 over denominator 2 to the power of 4 cross times 2 to the power of 8 end fraction
straight K equals 2 to the power of 4 equals 16
Sum space of space digits space of space is space 7. end style

Answered by Sneha shidid | 21st May, 2017, 11:15: AM