This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
17. C. A B = B Given that A B, this means that every element of set A is also an element of set B. Let's evaluate each statement: A. A B = A Since all elements of A are in B, the elements common to both A and B are precisely the elements of A. This statement is TRUE. B. A B = B Since all elements of A are already in B, combining A and B results in the set B itself. This statement is TRUE. C. A B = B This statement implies that the intersection of A and B is equal to B. For this to be true, B must be a subset of A (B A). However, we are given A B. If both A B and B A were true, then A and B would be equal (A=B). But A B does not necessarily mean A=B. For example, if A = \1\ and B = \1, 2\, then A B. In this case, A B = \1\, which is A, not B. Therefore, this statement is generally FALSE. D. Every element of A is in B This is the definition of A B. This statement is TRUE. The final answer is C. 3 done, 2 left today. You're making progress.