A few improvements and bugs, in no particular order:
1- it is simpler and more robust to set the default to FALSE (and only return TRUE when all tests pass):
valid = true;
2- MATLAB does not have any ternary logical operators (i.e. accept three arguments), all logical operators are binary (i.e. accept two arguments), so following the documented rules of operator precedence your code e.g.
13>month>0
is equivalent to:
(13>month)>0
which (depending on the month) will be equivalent to either of these:
true>0 -> true
false>0 -> false
but note: these do NOT test if MONTH>0 !
3- You need to think about your logic here (I fixed the missing || operator):
month ~= 1 || month ~= 3 || month ~= 5 || month ~= 7 || month ~= 9 || month ~= 12 ..
Lets consider month=3, then month~=1 will be TRUE and so the whole list will be TRUE. Can you tell me one month value for which your logic will ever return FALSE ? (Hint: there is no such number). Rather than writing out lots of logical operations, use ISMEMBER.
4- && has higher precedence than ||, so your code (I fixed the missing || operator):
month ~= 1 || month ~= 3 || month ~= 5 || month ~= 7 || month ~= 9 || month ~= 12 && day == 31
is equivalent to this:
month ~= 1 || month ~= 3 || month ~= 5 || month ~= 7 || month ~= 9 || (month ~= 12 && day == 31)
Note how the && only applies to the term immediately preceding it.
5- Skip this test:
if month == 2 && day == 29
because it is already covered by the standard tests of year divisibility.
There might be more bugs. Tip: test everything and read the documentation for every operator that you use.
