QUESTION $1$: $[13$ pts$]$ Using the black$-$box testing and in particular the equivalence partitioning method, we want to derive test cases for a program $P$ that verifies the validity of a birthday of a CIT student $($day$,$ month, year$)$ given as input.

The output of this program shall be one the two following messages: "VALID" or "NOT$-$VALID"

A date is valid if the day, the month and the year are valid.

A valid day would be $1$ and $30,$ or $31$

A valid month would be $1$ and $12,$

A valid year would be $1970$ and $2007$

a$)$ What are the equivalence classes of each input of the program P$?[5$ pts$]$

b$)$ How many test cases do we need to test this program with both strong equivalencepartitioning test? And with weak equivalence partitioning? $[2$pts$]$

c$)$ Derive the test cases for the weak equivalence partitioning in the format of a table? $[4$pts$]$

$\backslash$table$[[$day$,$month,year,$\backslash$table$[[$Valid$/$Not$],[$valid$]]],[,,,],[,,,],[,,,],[,,,],[,,,],[,,,],[,,,]]$

d$)$ Now, if we consider that February $($month$=2)$ can be only $28$ days, how many test cases do we need to test this program, For the Strong and for the weak equivalence partitioning $[2$pts$]$