Question

Write the set \[A=\left\{ x:x\in R,0\le x < 7 \right\}\] as an interval.

Answer 1

Hint: For solving this question you should know about the interval of a set. In this problem we will first discuss the interval of a set for any function and then we will find the necessary interval for the given problem.

Complete step by step answer:
According to the question it is asked to us to write the set \[A=\left\{ x:x\in R,0\le x<7 \right\}\] as an interval.
So, we can see that here we have to find the interval for the given set. And first of all we talk about what is an interval for a set.
So, generally we know that the interval is a period in which any set is defined or that gives proper required value within that interval or a period of fixed values. And this interval is different in representing the way. Generally the interval shown as \[\left( x,y \right)\] here x is the starting value and y is the ending or last value.
But it does not contain this starting value x and ending or last value y. It shows that we will take all the values which are available between these two numbers.
And if we have to take the starting or ending values or if we want to contain both the values then we will use the bracket ‘[’ for starting value and ‘]’ for containing ending value. So, generally if both x and y are in the interval then we can write as \[\left[ x,y \right]\].
According to our question set \[A=\left\{ x:x\in R,0\le x<7 \right\}\]. Here, we can see that ‘0’ is also containing in the interval and 7 is not in that so we can write it as,
\[x\in \left[ 0,7 \right)\]
So, the interval is \[\left[ 0,7 \right)\].

Note: While solving these types of questions you have to be careful about the bracket and curly braces. Both will be used separately if any one of them is not contained in the interval and if both are contained then we will use the bracket on both sides.