For-A-1-2-3-let-B-be-the-set-of-2-element-sets-belonging-to-P-A-and-let-C-be-the-set-consisting-of-the-sets-that-are-intersections-of-two-distinct-elements-of-B-Determine-C-P-A-power-set-

Question Number 42763 by Joel578 last updated on 02/Sep/18

$$\mathrm{For}\:{A}\:=\:\left\{\mathrm{1},\:\mathrm{2},\:\mathrm{3}\right\},\:\mathrm{let}\:{B}\:\mathrm{be}\:\mathrm{the}\:\mathrm{set}\:\mathrm{of}\:\mathrm{2}−\mathrm{element}\:\mathrm{sets} \\ $$$$\mathrm{belonging}\:\mathrm{to}\:{P}\left({A}\right)\:\mathrm{and}\:\mathrm{let}\:{C}\:\mathrm{be}\:\mathrm{the}\:\mathrm{set}\:\mathrm{consisting}\:\mathrm{of} \\ $$$$\mathrm{the}\:\mathrm{sets}\:\mathrm{that}\:\mathrm{are}\:\mathrm{intersections}\:\mathrm{of}\:\mathrm{two}\:\mathrm{distinct}\:\mathrm{elements} \\ $$$$\mathrm{of}\:{B}.\:\mathrm{Determine}\:{C} \\ $$$$ \\ $$$${P}\left({A}\right)\:=\:\mathrm{power}\:\mathrm{set}\:\mathrm{of}\:{A} \\ $$

Commented by Joel578 last updated on 02/Sep/18

$$\mathrm{I}\:\mathrm{got}\:\mathrm{the}\:\mathrm{answer}\:{C}\:=\:\left\{\left\{\mathrm{1}\right\},\:\left\{\mathrm{2}\right\},\:\left\{\mathrm{3}\right\}\right\} \\ $$$$\mathrm{Is}\:\mathrm{it}\:\mathrm{right}? \\ $$

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