Q 71. - Calculus

Question

Prove that $R^2$ is both an open subset and a closed subset of $R^2$. 

Step-by-Step Solution

Answer

It is proved that the a $R^2$ is both an open subset and a closed subset of $R^2$.

Step 1. Given information.

We have given set is $R^2$.

Step 2: Prove the given statement.

A subset is said to be open if it does not have a boundary to identify.

The given set is a universal set. It involves all the points in the space of $R^2$. It does not have any boundary to identify. So, it is an open set.

The complement of $R^2$ is an empty set, which is both open and closed set.

Thus, a $R^2$ is Both Open and Closed Set