Question

$\huge{\sf{question : - }}$
$\mathsf{ \red{Two \: finite \: sets \: have \: m \: and \: n \: elements.}}$
$\mathsf{ \red{ The \: total \: number \: of \: subsets \: of }}$
$\mathsf{ \red{the \: first \: set \: is \: 56 \: more \: than \: the }}$
$\mathsf{ \red{total \: number \: of \: subsets \: of \: the \: second \: set . }}$
$\mathsf{ \red{Find \: the \: values \: of \: m \: and \: n .}}$
A) m=6,n=2
B) m=6,n=3.
C) m=6,n=5
D) none​

Answer 1

Correct option is B [6,3]

Number of subsets of the set having m element is given by 2 m.

Number of subsets of the set having m element is given by 2 m. Thus number of subsets of the set having m element is 2 m and that having n element is 2n .

.According to the question, 2 m=2 n +56

.According to the question, 2 m=2 n +56⇒2 m−2 n=56

.According to the question, 2 m=2 n +56⇒2 m−2 n=56 ⇒2 n (2 m−n −1)=56

.According to the question, 2 m=2 n +56⇒2 m−2 n=56 ⇒2 n (2 m−n −1)=56⇒2 n (2 m−n−1)=8(8−1)=2 2(2 3−1)

−1) ⇒n=3 and m−n=3

−1) ⇒n=3 and m−n=3⇒m=n+3=3+3=6.

Answer 2

Answer:

b)

please mark me as a brain lies