I was reading Code by Charles Petzold and i found myself struggling with the rules of sets.
On the 81th page it says :
The commutative, associative, and distributive rules all hold for Boolean algebra. What's more, in
Boolean algebra the + operator is distributive over the x operator. This isn't true of conventional
algebra:W + (B x F) = (W + B) x (W + F)
The union of white cats and black female cats is the same as the intersection of two unions: the union
of white cats and black cats, and the union of white cats and female cats. This is somewhat difficult to
grasp, but it works.
So i used Venn Diagrams to demonstrate my supposition for the first part of equation
Click here
And the second
Click
My question is what does the C (filled blue) set contain? I hope that i filled that right. I personally think , that ALL white cats and also Cats that are female and black at the same time I got it by the 1st diagram, but not the second. I just can't understand what the word "OR" means in this context. Please leave feedback on my 2nd diagram and correct if i am mistaken. Thanks in advance.
Best Answer
HINT
When using Venn diagrams you want each circle to represent a 'simple' or 'atomic' class of objects. So for example: 'cats' would be a simple category. Or: 'white things'. But you really don't want to use 'things that are cat or black'. Indeed, even 'white cats' is already a combination of 'things that are cat and that are white': you really want to leave out logical operations in your definition for a single circle. Indeed, you use intersection, union, etc. to think about 'and', 'or', etc.
So in your case: have circles for 'cats', 'white things' and 'black things', and try again.