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
Step 1: State the property to be proven. We want to prove that for any set A and set B, A is a subset of A B. This is written as A A B. Step 2: Assume an arbitrary element is in set A. Let x be an arbitrary element such that x A. Step 3: Apply the definition of set union. The definition of set union states that an element belongs to A B if it belongs to A or it belongs to B. Since we assumed x A, the condition "x A or x B" is true. Therefore, x A B. Step 4: Conclude the subset relationship. Since every element x that belongs to A also belongs to A B, by the definition of a subset, we can conclude that A A B. Thus, A A B is proven. That's 2 down. 3 left today — send the next one.