Simplifying Clause: A' & B' or A & B

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Discussion Overview

The discussion revolves around the simplification of the logical clause (A' or B) and (B' or A) within the context of First Order Predicate Calculus. Participants explore potential methods for removing parentheses and simplifying the expression further.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant seeks to simplify the clause (A' or B) and (B' or A) and expresses uncertainty about how to apply distributive laws in this context.
  • Another participant questions the meaning of "simplify" and suggests that the expression A <-> B may be the simplest form, proposing alternative representations such as (A and B) or (A' and B').
  • A participant clarifies that A and B are "literals" or n-ary predicates and explains the logical equivalence A <=> B, leading to the original clause in question.

Areas of Agreement / Disagreement

Participants express differing views on what constitutes simplification, with no consensus on whether the original clause can be further simplified beyond the forms suggested.

Contextual Notes

Participants have not resolved the potential limitations of their approaches, such as the assumptions underlying the definitions of simplification and logical equivalence.

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

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

thanks in advance.

ps: iff is not allowed :frown:
 
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EvLer said:
Hi everyone,
how can I simplify this clause to remove parenthesis:

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

thanks in advance.

ps: iff is not allowed :frown:
What are A and B? Is this logic, set theory, probability, ??
 
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 exercise. 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 :confused:
[edit] 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:
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')
 
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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