# Proving two boolean expressions

#### 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

#### 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))