Subtracting sets? What does something like [A and (B - C)] mean, where A, B, C are sets?

A, B, and C are sets.





A has yellow, purple, and blue.


B has yellow, green, and black.


C has green, orange, and brown.





The union of A and B is yellow, purple, green, blue, and black. That's the total of everything in A and B.





The intersection of A and B is yellow.


That's what A and B has in common.





Suppose we have B - C.


B has yellow, green, and black.


C has green, orange, and brown.





B - C is {yellow, green, black} - {green, orange, brown}.


What do B and C have in common? Green.





Thus,


B - C is {yellow, green, black} - {green}.





Now, B - C = {yellow, black}.





All I did was that I took away the green.





Orange and brown has no effect on B because B doesn't have orange and brown.

Subtracting sets? What does something like [A and (B - C)] mean, where A, B, C are sets?
The difference of sets, like B - C usually means in B, but not in C.





If D = B-C, the A and D usually means the intersection of A and D, or, in both A and D.
Reply:B - C is the set of all ements in B that are NOT in C





A and B-C is their interaction, the set of elements that's in both A and B-C
Reply:that means you find first the relative complement of C with respect to B. and you find the intersection of the resulting set to set A.





relative complement of C wrt B are the elements of set B not in set C