- #1

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how can I simplify this clause to remove parenthesis:

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

thanks in advance.

ps: iff is not allowed

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- Thread starter EvLer
- Start date

- #1

- 458

- 0

how can I simplify this clause to remove parenthesis:

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

thanks in advance.

ps: iff is not allowed

- #2

honestrosewater

Gold Member

- 2,132

- 5

What are A and B? Is this logic, set theory, probability, ??EvLer said:

how can I simplify this clause to remove parenthesis:

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

thanks in advance.

ps: iff is not allowed

- #3

- 458

- 0

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

[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]

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)

further, implications (A -> B) are rewritten as: A'

so if i rewrite the logical equivalence i get: (A'

but i was wondering if it was possible to further simplify this clause

[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:

- #4

AKG

Science Advisor

Homework Helper

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- #5

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well, just was curios, that's all....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')

Thanks!

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