Question

★$\large {\bold {\bf {\blue {\underline {QUESTION}}}}}$★
Two finite sets have m and n elements. The total number of subsets of the first set is 56 more than the total number of subsets of the second set. Find the values of m and n.​

Answer 1

Answer:

m=6

n=3

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Answer 2

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$\boxed{\fcolorbox{red}{pink}{Question}}$

Two finite sets have m and n elements. The total number of subsets of the first set is 56 more than the total number of subsets of the second set. Find the values of m and n.

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• Let A has m elements

• Let B has n elements

Total number of students of A=2 m

Total number of students of B=2 n

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⇒2 m −2 n =562 n (2 m−n −1)=56

⇒2 n =even and 2 m−n −1=0 odd

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56=8×7=2 ^3 ×2 ^7

⇒2 n (2 m−n−1)=2 3×7

⇒n=3

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8(2 m−3−1)=8×7

⇒2 m−3^ −1=7

⇒2 m^−3 =8=2^3

⇒m−3=3

⇒m=6.

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