Q$10)$ A car dealer conducted a study on $100$ transactions during the period of one month,

and noticed that, $50$ customers were "young$-$age", $30$ customers were "middle$-$age", and

$20$ customers were "seniors". It also noticed that $70\%$ of "young$-$age" customers

purchased model A$,$ and $30\%$ purchased model B$.90\%$ of "young$-$age" customers

financed their cars. Furthermore, the car dealer noticed that the" middle$-$age" customers

purchased both models equally $(50\%-50\%.$ Only $20\%$ of the" middle$-$age" customers

financed their cars. The study also showed that $80\%$ of the "senior" customers purchased

model B$,$ and $20\%$ purchased model A$.$ They never financed their vehicles.

Finally, going through the financing accounts, the dealer noticed that $39$ Model A cars and

$12$ Model B cars were financed.

a$)$ Derive the co$-$occurrence matrix based on the transactions described above.

b$)$ Calculate support, confidence, and lift values for the following rules:

a$.$ Young$-$age customers finance their cars.

b$.$ Middle$-$age customers purchase model B$.$

c$)$ Which rule is strong? Why?