Question of symbols used in Boolean expressions

MrSoftware

Joined Oct 29, 2013
1,663
It's like asking would stop signs still work if they were painted green? Logically yes, but it would confuse a lot of people who are used to something else.
 

WBahn

Joined Mar 31, 2012
25,074
Please explain why, No?
It can be argued that we should not use + or · for Boolean operations at all because they carry along baggage associated with how we use them in arithmetic expressions. Some of that baggage is useful; namely anything that is familiar and that behaves the same. For instance.

A·0 = 0
A·1 = A
A+0 = A

These are all familiar to us but they are only valid for Boolean logic when we happen to use + for OR, · for AND, 0 for False, and 1 for True.

However, the baggage is detrimental when it makes us think that some things are true when they aren't or makes us forget that some things are true when we think they shouldn't be.

For instance, in Boolean algebra, AND, OR and NOT do not have a defined and widely agreed upon order of operations. But the +/· notation leads us to conclude that AND has higher precedence than OR and also that NOT, being a unary operator, has higher precedence than either. But this just isn't the case in general (though many computer programming languages make this the case but that is primarily a matter of conforming to how programmers tend to think so that fewer mistakes will get made).

Another thing that the arithmetic notation aids in is distributing AND over OR

A·(B+C) = A·B + A·C

But it hinders our ability to remember and apply the fact that OR also distributes over AND

A+(B·C) = (A+B)·(A+C)

because it "doesn't look right" to our senses owing to the fact that addition does not distribute over multiplication.

This is why purists use completely separate symbols for logical operators than for arithmetic operators.
 

Thread Starter

Joe Norris

Joined Aug 30, 2017
3
Thanks everyone for your replies
I am coming from an electrical engineering background, PLC programming and simple mathematical arithmetic equations.
So to explain this new context to 16+ yr old apprentices, I needed some assistance.
I had a feeling it was to do with the cross-discipline applications of the operators.

Thanks again.
 

eetech00

Joined Jun 8, 2013
1,785
Would it not make more sense if Boolean expressions used The + symbol as AND, & the . symbol as OR?
In Boolean algebra, the + symbol is the symbol for logical addition. A logical OR performs a functional equivalent.
The . (dot) symbol is the symbol for logical multiplication. A logical AND performs this functional equivalent.

Look up information on Boolean Algebra for more info.

eT
 

WBahn

Joined Mar 31, 2012
25,074
In Boolean algebra, the + symbol is the symbol for logical addition. A logical OR performs a functional equivalent.
The . (dot) symbol is the symbol for logical multiplication. A logical AND performs this functional equivalent.

Look up information on Boolean Algebra for more info.

eT
What do you mean by "logical addition" and "logical multiplication"?

Could you please define them and show how logical OR and logical AND are equivalent, respectively.

Be sure not to use a definition that basically amounts to calling an OR operation a "logical addition", but rather is based on defining "logical addition" without regard to OR/AND/NOT and then establishes that it is equivalent to OR.

If you want to define addition on a number system having just two values (i.e., a mod-2 world), then addition is performed by XOR and multiplication is performed by AND.
 
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