Final answer:
To construct the addition table for Z/4, list the elements {0, 1, 2, 3} and calculate the sums by adding pairs of elements, taking the result modulo 4 to ensure it falls within the set. The resulting table demonstrates all possible sums in Z/4.
Step-by-step explanation:
To construct the addition table for Z/4, we need to list all the elements in Z/4 and then find the sum of each pair of elements. Z/4, also known as the integers modulo 4, consists of the set {0, 1, 2, 3}. Each element represents an equivalence class of integers that are congruent to each other modulo 4.
Here is the addition table for Z/4:
+ 012300123112302230133012
To use this table, select one number from the top row and another from the leftmost column, then find their intersection. For example, 1 + 3 in Z/4 is found by looking at the intersection of the row starting with 1 and the column topped with 3, which is 0.
This is because when we add together two numbers and get a sum greater than or equal to 4, we subtract 4 from the sum until we get a result that is in our set {0, 1, 2, 3}. This process is known as 'taking the sum modulo 4.'