How can I come from NOT x AND y OR NOT z to two formulas: NOT x OR NOT z and NOT y OR z

Question

I dont understand how I come from

NOT x AND y OR NOT z 

to two formulas:

NOT x OR NOT z
NOT y OR z

Can somebody show me the rule? It should bring the first formula into CNF.

Thanks in advance.

Answer 1

It helps to have parentheses:

$$(\neg X \land Y) \lor \neg Z \Leftrightarrow (\neg X \lor \neg Z) \land (Y \lor \neg Z)$$

by the rule of (right-) Distribution

And yes, it is now in CNF.