Two finite sets have $m$ and $n$ elements. The total no. Q subset first set is $56$ more than the total no. of subsets of the second set. Find the values $m + n$ .

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$N u m b e r o f S u b s e t o f A = 2^{m} N u m b e r o f S u b s e t o f B = 2^{n} \Rightarrow 2^{m} - 2^{n} = 56 \Rightarrow 2^{n} (2^{m - n} - 1) = 2^{6} - 8 \Rightarrow 2^{n} (2^{m - n} - 1) = 2^{3} (2^{3} - 1) \Rightarrow n = 3 m - n = 3, m = 6 ∴ m + n = 6 + 3 = 9$

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Two finite sets have m and n elements. The total no. Q subset first set is 56 more than the total no. of subsets of the second set. Find the values m+n.

NumberofSubsetofA=2mNumberofSubsetofB=2n⇒2m−2n=56⇒2n(2m−n−1)=26−8⇒2n(2m−n−1)=23(23−1)⇒n=3m−n=3,m=6∴m+n=6+3=9

Two finite sets have $m$ and $n$ elements. The total no. Q subset first set is $56$ more than the total no. of subsets of the second set. Find the values $m + n$ .

$N u m b e r o f S u b s e t o f A = 2^{m} N u m b e r o f S u b s e t o f B = 2^{n} \Rightarrow 2^{m} - 2^{n} = 56 \Rightarrow 2^{n} (2^{m - n} - 1) = 2^{6} - 8 \Rightarrow 2^{n} (2^{m - n} - 1) = 2^{3} (2^{3} - 1) \Rightarrow n = 3 m - n = 3, m = 6 ∴ m + n = 6 + 3 = 9$