Final answer:
The relation defined in the set A = (1, 2, 3, 4) as a set of ordered pairs where relations = (x, y): x² + y² < 20 can be determined by finding all the possible ordered pairs (x, y) that satisfy the inequality x² + y² < 20. This inequality represents the region inside a circle with radius √20, centered at the origin. By substituting different values of x and y into the inequality, we can find all the ordered pairs that satisfy the inequality.
Step-by-step explanation:
The relation defined in the set A = (1, 2, 3, 4) as a set of ordered pairs where relations = (x, y): x² + y² < 20 can be determined by finding all the possible ordered pairs (x, y) that satisfy the inequality x² + y² < 20. This inequality represents the region inside a circle with radius √20, centered at the origin. By substituting different values of x and y into the inequality, we can find all the ordered pairs that satisfy the inequality.
For example, plugging in x = 1, we get 1 + y² < 20. Solving this inequality, we find that y² < 19, which means -√19 < y < √19. Therefore, for x = 1, the possible values of y that satisfy the inequality are between -√19 and √19.
We can repeat this process for other values of x and find all the ordered pairs that satisfy the inequality x² + y² < 20. The set of these ordered pairs will be the relation defined in the set A.