How do you simplify this expression?
$$\lnot[\lnot[(P \lor Q) \land R] \lor \lnot Q] \equiv Q \land R$$
I understand the laws used but still not getting the exact answer. I would appreciate if someone solved this for me.
Asked
Active
Viewed 121 times
0
-
In the future, please use MathJax to format your questions (I've cleaned up your post for you this time). Also, it is really helpful if you state the question in the actual body, in addition to in the title. Someone should be able to understand your question without having to read the title. – Xander Henderson Sep 16 '17 at 05:43
-
2What does it mean $A\lor \land B$? – caverac Sep 16 '17 at 05:48
-
@caverac that was a typo introduced in the MathJax edit, so I've fixed it according to the original. – Wildcard Sep 16 '17 at 05:57
1 Answers
0
\begin{eqnarray} \lnot[\lnot[(P\lor Q)\land R]\lor \lnot Q] &=& [(P\lor Q)\land R] \land Q \\ &=& [(P\land R)\lor (Q\land R)] \land Q \\ &=& (P\land R\land Q) \lor (Q\land R) \\ &=& (P\land A) \lor A ~~~\mbox{where}~~~ A = Q\land R\\ &=& A = Q \land R \end{eqnarray}
caverac
- 19,345
-
Equality 1: negation and De Morgan's Law.
Equality 2: distributive law.
Equality 3: distributive law.
Equality 4: re-labeling.
Equality 5: ??
– Jester Tran Sep 16 '17 at 06:34 -
1