Determine the domain of the relation R = {(19, 96), (20, 101), (21, 106), (22, 111)}.

The domain of a relation is the set of all first elements (also known as 'inputs' or 'x-values') in the ordered pairs of that relation. For the given relation R = {(19, 96), (20, 101), (21, 106), (22, 111)}, the domain would be the set of all the first elements of each ordered pair.

The domain of this relation R is: {19, 20, 21, 22}.

This is because each of these numbers appears as the first component in the ordered pairs, and it represents all possible input values in this particular relation.

Understanding domain and range is an important part of working with functions and relations in mathematics.

- Domain: The domain of a function or relation is the set of all possible input values (x-values) for which the function or relation is defined. - Range: The range, on the other hand, is the set of all possible output values (y-values) that can come from those inputs.

For example, consider the function y = 2x + 3. To find the domain of this function, you look for all the possible values of x. As there are no restrictions (such as division by zero or square roots of negative numbers), the domain is all real numbers (often symbolized by ℝ).

To find the range, you determine the possible values of y that can result from plugging the various x values into the function. For a linear function like y = 2x + 3 with no restrictions on the x-values, the range is also all real numbers.

Sometimes functions have restrictions on the domain. For instance, the function f(x) = 1/(x-2) does not allow for x to be 2, because it would cause division by zero. Hence, the domain of this function would be all real numbers except 2, often written as ℝ - {2}.

When given a set of ordered pairs, the domain and the range can be easily determined by looking at the first and second elements of each pair, respectively. It's important to list them without duplication and typically sets are written in ascending order, although the order of elements in a set does not affect its definition.