What is the difference between (A and B') and (B')? Read the set "A and not B" vs. "not B"
The words "and" and "or" have specific meanings in probability.
"and" is the union of two sets; to be in the union of two sets an object must be in both sets.
Usually "or" is the inclusive or; an object needs to belong to one of the two sets or it can belong to both sets. (In some applications we use the exclusive or or XOR; here the object must belong to one of the sets and not lie in the intersection.)
B' is the set of all objects that do not belong in set B.
A and B' is the set of all objects that are in set A and not in set B. (It isthe set of objects in A but not in the intersection of A and B.) This is written `A-(A nn B)` .
An object that is in neither A nor B belongs to B', but is not in A and B'.