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
Here are the definitions of sets A and B, and their common set operations. Step 1: Define set A. Set A is defined as the set of all x such that x is a positive integer. A = \x / x Z^+\ This means A includes all integers greater than 0. A = \1, 2, 3, 4, \ Step 2: Define set B. Set B is defined as the set of all x such that x is an integer and x is less than 0. B = \x / x Z and x < 0\ This means B includes all negative integers. B = \, -4, -3, -2, -1\ Step 3: Find the intersection of A and B (A B). The intersection of two sets contains elements that are common to both sets. Set A contains only positive integers. Set B contains only negative integers. There are no common elements between positive and negative integers. A B = The intersection of A and B is the empty set. A B = Step 4: Find the union of A and B (A B). The union of two sets contains all elements that are in either set (or both). Combining the elements of A and B: A B = \, -3, -2, -1, 1, 2, 3, \ This set includes all integers except for 0. This can be written as the set of all integers excluding 0. A B = Z \0\