Absorption Law with Negation

Question

Would absorption law work for statements with neagations in them like $( \neg q \land \neg r) \lor r$?

but isn't distributive law the case where the 3 variables are all different? — Extreme112, Dec 06 '14 at 04:02
According to wikipedia there is an absorption law that states that if $P \rightarrow Q$ then $P \rightarrow P \wedge Q.$ — recmath, Dec 06 '14 at 04:08
So if I simplified this would I get $(r \lor \neg q) \land (r \lor \neg r)$? — Extreme112, Dec 06 '14 at 04:11

score 2 · Accepted Answer · edited Dec 06 '14 at 04:30

2

Perhaps this is what you want: $$ ( \neg Q \land \neg R) \lor R = (\neg Q \lor R) \land (\neg R \lor R) $$

Note that $\neg R \lor R$ is always true, so the above becomes: $$\neg Q \lor R.$$

edited Dec 06 '14 at 04:30

Graham Kemp

answered Dec 06 '14 at 04:11

recmath

1 Answers1