Question

What is meant by “Open Convex Region”?

Answer 1

Hint: To solve this type of question we need to know the definition for the convex region and the definition for the non-convex region. Also, we need to know the differences between the convex region and non-convex region to solve this type of question. We need to know how to join the two or more points with the straight line.

Complete step by step solution:
In this question, we would explain the definition of convex region.
For explaining the definition of the convex region the following diagram will help us,

In the above figure, we have two points \[A\& B\] inside the \[C\] region. Also, the line segment joining the points \[A\& B\] is present inside the \[C\] region. A convex region is a region such that, for every pair of points is present within the region, every point on that straight line segment that joins the pair of the points is also present inside the region. So, we can define that the above-mentioned region is convex.
If every point on that straight line segment that joins the pair of the points is not present inside the region, that type of region is called a non-convex region. The figure which is given below is an example of a non-convex region.

In the above figure, we can see that the straight line which joins the point \[A\& B\] is present outside of the region. So, the above region is the non-convex region.

Note: Note that the line which joins the two-point in the region must be straight. Also, note that if every point is present inside the region and every straight line segment joining the two points is present inside the region, then the region is called a convex region, otherwise it is called the non-convex region.