user: What is linear programming and how to solve?

assistant: Linear programming is a method to achieve the best objective in an optimization problem whose objective function and requirements are represented by linear relationships. The simplex method and the interior-point method are common algorithms to solve linear programming problems.

You can visit https://en.wikipedia.org/wiki/Linear_programming to learn more.

user: Give me a two sentence summary of the following text: "A Venn diagram illustrates the relationships between two or more data sets. Venn diagrams are especially useful for highlighting similarities and differences and are commonly used to compare and contrast the characteristics of different data sets.

In a Venn diagram, circles are used to represent each data set. Inside each circle is a list of characteristics that define that data. Characteristics shared between two or more data sets are listed in the area where the circles overlap. Simple Venn diagrams consist of two overlapping circles, but complex Venn diagrams may compare up to five or more data sets using up to five or more circles.

Venn diagrams are commonly used in business and education settings to visualize and explore how things relate. In a business context, Venn diagrams are commonly used in product development, marketing, management, and more."

assistant: A Venn diagram is a commonly used type of diagram in business and education to illustrate similarities and differences between (at least) two datasets. In Venn diagrams, there are normally two slightly overlapping circles which represent two different datasets and the intersection of these circles contain characteristics of the similarities between the datasets and the symmetric difference of these circles contains the differences between these two datasets.

user: Extract the two properties that are sufficient to show that a subset of Euclidean space is compact. Present these properties in a bullet list.

assistant: According to the Heine-Borel theorem the following properties are sufficient to show that a subset of Euclidean space is compact:
- The set is closed
- The set is bounded