# Boolean Algebra

• May 27th 2012, 02:05 AM
BabyMilo
Boolean Algebra
How do you simplify this

not p and q or p and not q or p and q

http://www4a.wolframalpha.com/Calcul...=18&w=199&h=18

http://www4a.wolframalpha.com/Calcul...47&w=167&h=228

thanks.
• May 27th 2012, 12:47 PM
emakarov
Re: Boolean Algebra
Quote:

Originally Posted by BabyMilo
How do you simplify this

not p and q or p and not q or p and q

Could you disambiguate this expression using parentheses?

Quote:

Originally Posted by BabyMilo

The usual place for problems about Boolean algebra is the Discrete Mathematics subforum.
• May 27th 2012, 01:05 PM
BabyMilo
Re: Boolean Algebra
No could you please show me?
can not find it anywhere.
• May 27th 2012, 01:38 PM
emakarov
Re: Boolean Algebra
Boolean operations "not," "and" and "or" are similar to arithmetic operations of negation, multiplication and addition. For arithmetic, we have rules saying which operations are performed first. For example, multiplication is performed before addition. Boolean algebra is less common and there is a wider variety of conventions concerning which operation is performed first. Therefore I am asking you to make this expression unambiguous by inserting some parentheses.

OK, in fact there is a more-or-less standard order of operations for Boolean algebra, though it is probably still less standard than for arithmetic. However, since your expression does not have any parentheses, I somehow doubt that this standard order can be used here. Before I spend time on analyzing the expression, I'd like to be sure that the expression is the correct one.

Now, you can't mathematically solve the problem of which operation is performed first. This is a matter of definition. To find this definition, you have to go to the source from which this problem comes.