Question

Express the following set as an interval: \[F = \left\{ {x:x \in R - 2 \leqslant x < 0} \right\}\]

Answer 1

Hint: A set is a collection of objects where each object in the set is called an element for that set denoted by \[x \in R\]where x is the element of the set R and set having no elements to them is called an empty set. An interval is a set number that consists of all real numbers between a given pair of numbers. An endpoint of an interval is either of the two points that mark the endpoint of a line segment. An interval can be of different types which can include either endpoint or both endpoints or neither endpoint.
An interval that does not include endpoints is an open interval denoted by round brackets (). For closed intervals, they include endpoints of the interval, and they are denoted by square bracket []. Any interval which includes either of the endpoints is denoted by (].
In the question we need to define the interval of the given function with proper limits for which we will use the different brackets

Complete step-by-step solution
In the given set \[F = \left\{ {x:x \in R - 2 \leqslant x < 0} \right\}\]
Where x is a real number which is in the interval of\[ - 2 \leqslant x < 0\], represented on a number line

From the set, if interval, it is clear that the set does not include the number 0; hence it will be denoted by open interval whereas -2 is included in the set; hence the set of the interval can be represented as
\[x \in \left[ { - 2,\left. 0 \right)} \right.\]

Note: The interval notation is a way of representing subsets of the real number line where a closed interval is one that includes its endpoints, and an open interval is one that does not include its endpoints.