# 1. Verify whether the system is a Boolean algebra.

Discussion in 'Homework Help' started by audreyeckman, Jan 19, 2016.

1. ### audreyeckman Thread Starter New Member

Jan 7, 2016
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0
I am really struggling with this problem, and so are my friends in the same course. Please refer to PDF for the tables.
Any help or guidance is appreciated!

Given a mathematical system M=({0,a,b,c},#, &) where the two operators # and

& are defined in the following two subtables.

1. Verify whether the system is a Boolean algebra.

2. List the complements of elements 0, a, b, and c if the system is a Boolean algebra.

I have started a table that my professor suggested to follow on the pdf, but I have no idea how to start it.

Another hint was that:

I found the following link is quite useful.

http://www.ctp.bilkent.edu.tr/~yavuz/BOOLEEAN.html

In table 1.(b), you can find something like very similar to "0" in table 1.(a).

Now you can say following:

(1) Something # Something' = 0 or a or b or c,

(2) Something & Something' = 0 or a or b or c.

From table 1.(a) and 1.(b), you can find pairs that satisfy your (1) and (2) always.

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2. ### WBahn Moderator

Mar 31, 2012
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The first step is to make sure you understand what is required for something to be "a Boolean algebra".

So what, in YOUR words, is required?

3. ### audreyeckman Thread Starter New Member

Jan 7, 2016
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0
Following the commutative, distributive, and identity laws is required I believe.

4. ### WBahn Moderator

Mar 31, 2012
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5. ### Papabravo Expert

Feb 24, 2006
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The laws that the operators must follow are only part of the story. The properties of the elements are also important.