A\(B ∩ C) ⊆(A\B) ∩ (A\C)

How can I show this on a diagram?

How can I draw a diagram for this set?

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- Jun 19th 2012, 12:03 AMserhanbenersets
A\(B ∩ C) ⊆(A\B) ∩ (A\C)

How can I show this on a diagram?

How can I draw a diagram for this set? - Jun 19th 2012, 03:37 AMemakarovRe: sets
You have two sets, not one: A \ (B ∩ C) and (A \ B) ∩ (A \ C).

I assume you mean Venn diagrams. Do you know how to show anything on a Venn diagram, such as the set A or B ∩ C? If not, then you need to read a textbook. If yes, then what exactly is your difficulty in drawing these slightly more complicated sets?

I believe the inclusion you wrote is false in general. It would be true and, in fact, in would be an equality if ∩ is replaced by ∪ in the right-hand side. - Jun 19th 2012, 04:38 AMserhanbenerRe: sets
Yes I know how to show anything on a Venn diagram. But I can't show the example above.

- Jun 19th 2012, 05:38 AMemakarovRe: sets
Attachment 24104

(The picture is clickable.)

In the left picture, B ∩ C is blue and A is red. The part of A that is just red, i.e., does not include the central purple region, is A \ (B ∩ C).

In the right picture, A \ B is red and A \ C is blue. The purple intersection is (A \ B) ∩ (A \ C).

You can see that the purple part in the right picture is a subset of a purely red part of the left picture, i.e., (A \ B) ∩ (A \ C) ⊆ A \ (B ∩ C). Also, the purely red part of the left picture equals the painted part of the right picture, i.e., (A \ B) ∪ (A \ C) = A \ (B ∩ C). - Jun 21st 2012, 02:19 AMserhanbenerRe: sets
Many Thanks. I think there is a problem with the question."A\(B ∩ C) ⊆(A\B) ∩ (A\C)" seems to be wrong.