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Question: Two finite sets have m …

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Question: Two finite sets have m and n element. The number of subset of the first set is 112 more than that of the second. Find the value of m and n.

Posted by Ravi Sundriyal 4 years, 7 months ago

CBSE > Class 11 > Mathematics

1 answers

Sia ? 4 years, 7 months ago

We know that, for any given set having m elements, the number of subsets can be represented as 2^m
According to the given condition,
2^m = 112 + 2ⁿ
{tex}\Rightarrow{/tex} 2^m- 2ⁿ = 112 = 128 - 16
{tex}\Rightarrow{/tex} 2^m- 2ⁿ = 2⁷ - 2⁴ (as 2⁷=128 and 2⁴= 16 )
On comparing both the sides,
2^m= 2⁷ and 2ⁿ = 2^{4

{tex}\therefore{/tex}} m = 7 and n = 4

2Thank You

ANSWER

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CBSE > Class 11 > Mathematics