# What is the difference between (A and B') and (B')? Read the set "A and not B" vs. "not B"

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embizze | Certified Educator

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'.