Searching for preimage I found that the second rule is true: http://mathprelims.wordpress.com/category/topology/page/2/
I think that this must be true, because for every x in V there is only one y. But the other one is not true, because there can be more than one x's in V that have the same y...
Yes, that is right.
I didn't know the English translation of these terms, although now I see that the Dutch word is a literal translation of the word image. Pre-image is called the complete image in Dutch.
I am sorry if I didn't formulate the question properly, I had to translate this from Dutch, I don't know if range and domain are the proper terms. The question is about any function in general from V to W without any further specifications.
I would think that these statements are both untrue...
Given is the function of Set V towards Set W where A is a subset of V and B is a subset of W.
Questions:
Does the range of the complement of A equal the complement of the range of A?
Does the domain of the complement of B equal the complement of the domain of B?I am not entirely sure how to...
The hint and the size relationship confused me. I don't see how to solve this problem as an equation of x and given the fact that C is twice as large as B and three times as A, but I guess it is possible. If someone sees it, I am curious how to proceed.
There is no follow up question to this...
Problem:
-The Union of set A, set B and set C has 104 elements.
-The Union of Set A and B has 51 elements
-The Union of Set A and C has 84 elements
-The Union of Set B and C has 97 elements
-The Intersection of Set A and the Union of Set B and C has 17 elements.
-Set C has twice as many...