# Boolean Algebra Union and Intersection

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.

• "OR" is set union: "Cats are either male or female" means that the set of all Cats is "made of" the set of male Cats "plus" (set union) the set of female Cats. – Mauro ALLEGRANZA Apr 2 '17 at 11:43
• "AND" is set intersection : male Cats are both male and cats, i.e. they are the intersection of the set of all Cats with the set of all male "animals". – Mauro ALLEGRANZA Apr 2 '17 at 11:44
• Your first Venn diagram must be redraw: W + (B x F) does not "cover " all Cats. We have also Black male Cats (that are neither White nor Black female). – Mauro ALLEGRANZA Apr 2 '17 at 11:47