# Clause simplification

#### EvLer

Hi everyone,
how can I simplify this clause to remove parenthesis:

(A' or B) and (B' or A) ?

ps: iff is not allowed

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#### honestrosewater

Gold Member
EvLer said:
Hi everyone,
how can I simplify this clause to remove parenthesis:

(A' or B) and (B' or A) ?

ps: iff is not allowed
What are A and B? Is this logic, set theory, probability, ??

#### EvLer

A and B are "literals" as the book refers to them or n-ary predicates.
Sorry, should have specified: it's First Order Predicate Calculus. This isn't really an excersize. It's just that I saw that logical equivalence
A <=> B
can be rewritten as: (A -> B) and (B -> A);
further, implications (A -> B) are rewritten as: A' or B;
so if i rewrite the logical equivalence i get: (A' or B) and (B' or A)
but i was wondering if it was possible to further simplify this clause
 i know how to apply distributive laws in cases like this:
(A and B) or C
or similar, but not sure how that might work in clause with 4 predicates [/edit]

Last edited:

#### AKG

Homework Helper
What do you mean by "simplify"? It seems to me that A <-> B is the simplest form. You could write it as (A and B) or (A' and B')

#### EvLer

AKG said:
It seems to me that A <-> B is the simplest form. You could write it as (A and B) or (A' and B')
well, just was curios, that's all....

Thanks!

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