Proving two boolean expressions

Thread Starter

arashb

Joined Oct 5, 2007
2
Hi,

I am trying to prove two boolean expressions by using algebraic simplification.

I am trying to prove:

1) ((-a -> -b) /\ (a != b)) \/ ((a /\ c) -> (b /\ c))

2) (if b then P else if b then Q else R) = (if b then P else R)

I have proved both using truth tables, but haven't yet using algebra.

I have tried, but keep going in circles back to the original expression. Any help would be great.

Thnks
 

Dave

Joined Nov 17, 2003
6,970
Firstly, I'm confused by the terminology in your expression; what to the symbols "-", "->", "/\" and "\/" mean?

Secondly, can you upload your workings so we can have a look? It is easier to guide you on your current attempts rather than teach you a whole something new.

Dave
 

Thread Starter

arashb

Joined Oct 5, 2007
2
- means NOT
-> means implies
/\ means AND
\/ means OR


For the second expression, I have simplified it down to
(B /\ P) \/ (-B /\ ((B /\ Q) \/ (-B /\ R) ) = (B /\ P) \/ (-B /\ R))

so I am trying to show that (B /\ Q) \/ (-B /\ R) = R

The first, I have written it as

( (a \/ -b) /\ ((a /\ -b) \/ (-a /\ b))) \/ ((-a /\ c) \/ (b /\ c))
 
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