Creating Euler diagrams in math

[aburchett]

Create a Euler diagram to determine whether the syllogism is valid or invalid.

All children like games.
John likes games.
Therefore John is a child

What does the diagram look like and is this statement valid or invalid?

 

[soroban]

Hello, aburchett!

The problem is straight-forward if you're familiar with Euler diagrams and logic statements.
If you're not, you should not have been assigned this problem.
So exactly where is your difficulty?

Create a Euler diagram to determine whether the syllogism is valid or invalid.

. . All children like games.
. . John likes games.
. . Therefore, John is a child.

What does the diagram look like and is this statement valid or invalid?

"All children like games."
This means that the Child region is completely inside the Games region.

      * - - - - - - - - - - * 
      | Games               |
      |       * - - - - *   |
      |       |  Child  |   |
      |       |         |   |
      |       |         |   |
      |       * - - - - *   |
      |                     |
      * - - - - - - - - - - *

"John like games."
This means that John is inside the Games region.

      * - - - - - - - - - - * 
      | Games               |
      |                     |
      |                     |
      |                     |
      |   J                 |
      |                     |
      |                     |
      * - - - - - - - - - - *

"Therefore, John is a child."
This means that John is inside the Child region.

      * - - - - - - - - - - * 
      | Games               |
      |       * - - - - *   |
      |       |  Child  |   |
      |       |         |   |
      |   J   |         |   |
      |       * - - - - *   |
      |                     |
      * - - - - - - - - - - *

Obviously, the conclusion is not valid.