if X is a finite set. Let P(X) denote the set of all subsets of X and let n(X) denote the number of elements in X. If for two finite subsets A, B, n(P(A)) = n(P(B))+15 then n(B) = ........., n(A)=...........

Question

if X is a finite set. Let P(X) denote the set of all subsets of X and let n(X) denote the number of elements in X. If for two finite subsets A, B, n(P(A)) = n(P(B))+15 then n(B) = ........., n(A)=........... (A) 6, 2 (B) 8, 4 (C) 0, 4 (D) 0, 1

Tardigrade Admin · Accepted Answer

Let n(A) =m, n(B) =n n[P(A)] =2m.n [P(B)] =2n n[P(A)] =n[P(B)] +15 ⇒ 2m -2n =15 ⇒ m =4;n =0

Q. if X is a finite set. Let $P (X)$ denote the set of all subsets of $X$ and let $n (X)$ denote the number of elements in $X$ . If for two finite subsets $A, B, n (P (A)) = n (P (B)) + 15$ then $n (B) = ........., n (A) = ...........$

$6, 2$

$8, 4$

$0, 4$

$0, 1$

Let $n (A) = m, n (B) = n$
$n [P (A)] = 2^{m} . n [P (B)] = 2^{n}$
$n [P (A)] = n [P (B)] + 15$
$\Rightarrow 2^{m} - 2^{n} = 15 \Rightarrow m = 4; n = 0$

Q. if X is a finite set. Let P(X) denote the set of all subsets of X and let n(X) denote the number of elements in X. If for two finite subsets A,B,n(P(A))=n(P(B))+15 then n(B)=.........,n(A)=...........

6,2

8,4

0,4

0,1