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Question Number 94705 by s.ayeni14@yahoo.com last updated on 20/May/20

a set X had one more subset than set Y. If X has 8 more subsets than Y. Find the number if element in the set X.

$$\mathrm{a}\:\mathrm{set}\:\mathrm{X}\:\mathrm{had}\:\mathrm{one}\:\mathrm{more}\:\mathrm{subset}\:\mathrm{than}\:\mathrm{set}\:\mathrm{Y}. \\ $$$$\mathrm{If}\:\mathrm{X}\:\mathrm{has}\:\mathrm{8}\:\mathrm{more}\:\mathrm{subsets}\:\mathrm{than}\:\mathrm{Y}.\:\mathrm{Find}\:\mathrm{the}\:\mathrm{number}\:\mathrm{if}\:\mathrm{element}\:\mathrm{in}\:\mathrm{the}\:\mathrm{set}\:\mathrm{X}. \\ $$

Commented by prakash jain last updated on 20/May/20

I think your question is not correct If a set has n element then it has 2^n subsets. If Y haz k elements X has 1 more element than Y then X has k+1 elements X has 8 more subsets than Y 2^(k+1) =2^k +8 ⇒k=3 set X has k+1=4 elements

$$\mathrm{I}\:\mathrm{think}\:\mathrm{your}\:\mathrm{question}\:\mathrm{is}\:\mathrm{not} \\ $$$$\mathrm{correct} \\ $$$$\mathrm{If}\:\mathrm{a}\:\mathrm{set}\:\mathrm{has}\:{n}\:\mathrm{element}\:\mathrm{then}\:\mathrm{it} \\ $$$$\mathrm{has}\:\mathrm{2}^{{n}} \:\mathrm{subsets}. \\ $$$$\mathrm{If}\:\mathrm{Y}\:\mathrm{haz}\:{k}\:\mathrm{elements} \\ $$$$\mathrm{X}\:\mathrm{has}\:\mathrm{1}\:\mathrm{more}\:\mathrm{element}\:\mathrm{than}\:\mathrm{Y} \\ $$$$\mathrm{then}\:\mathrm{X}\:\mathrm{has}\:{k}+\mathrm{1}\:\mathrm{elements} \\ $$$$\mathrm{X}\:\mathrm{has}\:\mathrm{8}\:\mathrm{more}\:\mathrm{subsets}\:\mathrm{than}\:\mathrm{Y} \\ $$$$\mathrm{2}^{{k}+\mathrm{1}} =\mathrm{2}^{{k}} +\mathrm{8} \\ $$$$\Rightarrow{k}=\mathrm{3} \\ $$$$\mathrm{set}\:\mathrm{X}\:\mathrm{has}\:{k}+\mathrm{1}=\mathrm{4}\:\mathrm{elements} \\ $$

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