prove that AnB= null is equal to AcB'
Answers
Answer:
I'm typing on my phone so no Latex but I'll outline my argument as best as I can.
This implication is not true for all arbitrary sets. Let A = {1, 2} and B = {1, 2, 3}. A is a subset of B. The intersection of A and B is the set {1, 2} = A which is non-empty. So the implication is false.
However just for the sake of education let us assume that A is a subset of B and the intersection is the empty set for some sets A and B (notice this is a very different statement than the one you had in the question). We can infer from this that A must be the empty set. (B can be any set, including the empty set for this implication to be true).
The line of reasoning is loosely that if the intersection is empty then they can not have any shared elements between A and B. However because A is a subset of B we know that each element of A is also in B. The only way for both to be true is if A does not contain any elements
Answer:
sorry I don't know the answer