SOLUTION: When A ⊆ B the difference B \ A is defined to be the set of all objects that are in A but not in B. Construct a counterexample to the statement ”Given A ⊆ B ⊆ C,

Algebra ->  Proofs -> SOLUTION: When A ⊆ B the difference B \ A is defined to be the set of all objects that are in A but not in B. Construct a counterexample to the statement ”Given A ⊆ B ⊆ C,      Log On


   

Question 1016956: When A ⊆ B the difference B \ A is defined to be the set of all objects that are in A but not in B.
Construct a counterexample to the statement ”Given A ⊆ B ⊆ C, C \ (B \ A) = (C \ B) \ A”.
Answer by richard1234(7193) About Me  (Show Source):
You can put this solution on YOUR website!
"B \ A is defined to be the set of all objects that are in A but not in B."
It is defined the other way around, i.e. B\A is the set of elements in B but not A.

When A = {1}, B = {1,2}, and C = {1,2,3}, then

B \ A = {2} --> C \ (B \ A) = {1,3}
C \ B = {3} --> (C \ B) \ A = {3}