# E-book missing Boolean OR-over-AND distributive property

Discussion in 'Feedback and Suggestions' started by WBahn, Dec 1, 2014.

1. ### WBahn Thread Starter Moderator

Mar 31, 2012
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I think I have brought this up before, but am not sure.

The E-book includes the distributive property of AND over OR, namely

A(B+C) = AB + AC

But fails to mention the distributive property of OR over AND, namely

A+BC = (A+B)(A+C)

This is a very useful property that most people don't know about because it goes against the fact that we have long sense internalized the notion that addition does not distribute over multiplication the way that multiplication distributes over addition.

As an aside, I don't think it is a good idea to call the OR operation "addition" and the AND operation "multiplication" for just this reason. We are not adding or multiplying anything -- we are ANDing and ORing. We are merely using the same symbols for these operations as we do for addition and multiplication. I think that misusing the names of the arithmetic operations in place of the Boolean algebraic ones leads to the misperception that the rules of arithmetic algebra and those of Boolean algebra are the same when, clearly, they aren't. This is one of the reasons why more math-oriented treatments use different symbols (¬, ∧, ∨) and operation names (negation, conjunction, disjunction) entirely

But that's a pedagogical point that I'm sure has proponents on both sides aplenty.

2. ### Georacer Moderator

Nov 25, 2009
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I like this change, but it's a pretty major re-write, so we could use some more input. Is anyone else for or against?

3. ### WBahn Thread Starter Moderator

Mar 31, 2012
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There's actually two changes recommended. The first (adding the second distributive property) should be pretty simple and straightforward and non-controversial. The second, cleaning up the terminology, is certainly more involved. I would not recommend using the more math-oriented notation, but rather just using the logic terminology instead of the arithmetic terminology. But I would recommend putting a section near the front that covers all three so that people coming here having only seen one have somewhere to start so that they can follow the one that the E-book then proceeds to use.

4. ### tshuck Well-Known Member

Oct 18, 2012
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I think the addition of the property is warranted and should be included, however, I have to disagree with changing the notation, that is what most people will see in the field, which may be a disservice to those attempting to learn here.

WBahn's suggestion of adding a section to explain and introduce the different notations seems like a good idea, and would help clarify some of the problems some people have in discerning the meaning of the symbols.

It may be helpful to intersperse the various notations in the book and exercises, but that would require more work from whoever makes the change.

5. ### WBahn Thread Starter Moderator

Mar 31, 2012
18,093
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Note that I'm not recommending that we don't use the arithmetic notation, just the terminology to the degree that we would talk about ANDing the variables A and B instead of 'multiplying' the variables A and B. It would still be written as AB or A·B or A*B, it would just be described using predominantly the logical terminology instead of the arithmetic one.

6. ### tshuck Well-Known Member

Oct 18, 2012
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In that case, I support this idea. I think referring to Boolean operations using familiar, mathematical terms introduces a number of presumptions that, specifically in the case mentioned above, can prove to confuse the reader.