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Question Number 22652 by Tinkutara last updated on 21/Oct/17

$$\mathrm{Find}\mathrm{the}\mathrm{number}\mathrm{of}\mathrm{unordered}\mathrm{pairs}$$$$\{A,B\}(\mathrm{i}.\mathrm{e}.,\mathrm{the}\mathrm{pairs}\{A,B\}\mathrm{and}\{B,A\}$$$$\mathrm{are}\mathrm{considered}\mathrm{to}\mathrm{be}\mathrm{the}\mathrm{same})\mathrm{of}$$$$\mathrm{subsets}\mathrm{of}\mathrm{an}n-\mathrm{element}\mathrm{set}X\mathrm{which}$$$$\mathrm{satisfy}\mathrm{the}\mathrm{conditions}:$$$$\left(\mathrm{a}\right)A\ne B;$$$$\left(\mathrm{b}\right)A\cup B=X$$$$[\mathrm{e}.\mathrm{g}.,\mathrm{if}X=\{a,b,c,d\},\mathrm{then}\{\{a,b\},$$$$\{b,c,d\}\},\{\left\{a\right\},\{b,c,d\}\},\{\varphi ,\{a,b,c,d\}\}$$$$\mathrm{are}\mathrm{some}\mathrm{of}\mathrm{the}\mathrm{admissible}\mathrm{pairs}.]$$

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