LinkBack URL
About LinkBacksA\(B ∩ C) ⊆(A\B) ∩ (A\C)
How can I show this on a diagram?
How can I draw a diagram for this set?
You have two sets, not one: A \ (B ∩ C) and (A \ B) ∩ (A \ C).Originally Posted by serhanbener
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.
(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).
  |
