# Converting into CNF

I am still a bit confused by how to convert into CNF even though I have the rules written down.

How do I convert the following sentence into CNF?

$$(I \lor M) \Rightarrow H$$

I know I need to get rid of the implication symbol and when its in the form $$(I \Rightarrow H)$$ or $$(M \Rightarrow H)$$ then I can see how to do it, but when its one sentence like this how do I factor out the implication?

The reason I am stuck is because I do not know how to get rid of the resulting or:

$$(\neg I \lor H) \lor (\neg M \lor H) \Rightarrow I$$ think the OR here needs to be an AND to be CNF

Thanks

We have that $$A \Rightarrow B$$ is same with $$\neg A \lor B$$. This gives, that $$(I \lor M)\Rightarrow H$$ is same with $$\neg(I \lor M)\lor H$$.
And we have that $$\neg(I \lor M)$$ is same with $$\neg I \land \neg M$$
Putting together we have that $$(I \lor M)\Rightarrow H$$ is same with $$\neg I \land \neg M \lor H = (\neg I \land \neg M) \lor H = (\neg I \lor H) \land (\neg M \lor H )$$.
• For first comment (about CNF) I added to answer last equality. For last: $(I \lor M)\Rightarrow H$ is false if and only if when $I \lor M$ is true and $H$ is false. All other combinations gives implication true. – zkutch Feb 7 at 9:01
• Let be little more careful: $\neg(I \land M)$ is not same with $I \lor M$, but with $(\neg I) \lor (\neg M)$. And $\neg(I \lor M)$ is same with $(\neg I) \land (\neg M)$. So sentence "TV ON or LIGHTS ON, then ELECTRICITY BEING USED" is same with "(TV NOT ON and LIGHTS NOT ON) or ELECTRICITY BEING USED" – zkutch Feb 7 at 11:02