Case I: When we know that All X are Y
(i) No X is Y — not possible
(ii) Some X are Y — certain
(iii) Some X are not Y — not possible
(iv) All X are not Y — not possible
Case II: When we know that No X is Y
(i) All X are Y — not possible
(ii) Some X are Y — not possible
(iii) Some X are not Y — certain
(iv) All X are not Y — certain
Case III: When we know that Some X are Y
(i) All X are Y — possible
(ii) No X is Y — not possible
(iii) Some X are not Y — possible
(iv) All X are not Y — possible
Case IV: When we know that Some X are not Y
(i) All X are Y — not possible
(ii) No X is Y — possible
(iii) Some X are Y — possible
(iv) All X are not Y — possible
Case V: When we have no conclusion between X and Y
(i) All X are Y — possible
(ii) No X is Y — possible
(iii) Some X are Y — possible
(iv) Some X are not Y — possible
(v) All X are not Y — possible
Note: Since certainty means 100% possibility, all cases of certainty also qualify to be considered as possible