Question

The inclusive class interval are also called:
(A) discontinuous class intervals
(B) continuous class intervals
(C) unequal class intervals
(D) higher class intervals

Answer 1

Hint: We will first write the general form of inclusive class interval. Then, determine its nature by writing its roaster form. Also, we will plot the interval by taking any relevant example of inclusive class interval to select the correct option.

Complete step-by-step answer:
The inclusive class interval is of the form $\left[ {a,b} \right]$.
Here, both the numbers are included in the sets, that is, \[a\] and \[b\].
In the roaster form, we can write it as $\left\{ {x:a \leqslant x \leqslant b} \right\}$
The above representation does not represent a discontinuous class as it includes all the elements from $a$ to $b$.
If we have an interval for example, $\left[ {2,3} \right]$, then it includes all the real numbers from point 2 to 3.
If we represent this on a number line, we will get,

The interval $\left( {2,3} \right)$ is represented by a continuous line.
Hence, the inclusive intervals are also known as continuous class intervals.
Thus, option B is correct.

Note: The interval of the type $\left( {a,b} \right)$ is when $a$ and $b$ are included in the interval but still is a continuous class interval. Unequal class interval is the case when the length of class intervals are not the same.