Final answer:
The result of using complements in mathematics simplifies subtraction in arithmetic, and in set theory, it refers to elements that are not part of a given subset within a universal set.
Step-by-step explanation:
The result of using complements in mathematics depends on the context in which they are used. For example, in arithmetic, complements are used for simplifying subtraction; the 10's complement of a number is the difference between that number and the next power of 10, which helps in subtraction operations done by hand or in digital electronics. In the context of set theory, a complement refers to the elements not in the subset but within a larger universal set; highlighting the relationship between set elements.
Arithmetic Complements
In arithmetic, using complements can make manual subtraction faster. If we have to subtract 567 from 1000, we can find the 10's complement of 567, which is 433, and add it to the minuend (1000 in this case) to easily determine the result.
Set Theory Complements
In set theory, the complement of a set A (denoted as A') consists of all the elements that are in the universal set but not in set A. This concept is fundamental in understanding Venn diagrams and the relationships between different sets.