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Homework Statement
Hi, the problem states to draw a Venn Diagram for [itex]A\cap(BC)[/itex]
Homework Equations
[itex](B  C)[/itex] means include all elements in the set [itex]B[/itex] that are not in [itex]C[/itex].
Definition from my book: Let A and B be sets. The difference of [itex]A[/itex] and [itex]B[/itex], denoted by [itex]A  B[/itex], is the set containing those elements that are in A but not in B. The difference of [itex]A[/itex] and [itex]B[/itex] is also called the complement of [itex]B[/itex] with respect to [itex]A[/itex].
[itex]A\cap(BC)[/itex] means that after finding [itex](B  C)[/itex], find where [itex]A[/itex] intersects [itex](B  C)[/itex].
The Attempt at a Solution
Step 1:
[itex](B  C)[/itex]
(See png file called "step1")
Step 2:
[itex]A\cap(BC)[/itex]
(see png file called "step2")
My question is, do i shade in region 5, even though [itex](B  C)[/itex] means "no elements in [itex]C[/itex]" but when I have to show [itex]A[/itex] and [itex]B[/itex] intersect, I shade in region 4 obviously, but does that include region 5 because that's also where [itex]A[/itex] and [itex]B[/itex] intersect, but [itex]C[/itex] is also intersecting there as well.
So, in case you didn't follow because I may or may not be good at explaining things, should I include region 5 or exempt it from being shaded in?
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