Definition 2.3.2.
A \(\mathbb{P}\)SET is a collection of 3 cards such that the cards may be flipped over in such a way so that both the top and the bottom form SETs.
Section 2.3 P(rojective) SET
Each \(\mathbb{P}\) card consists of two SET cards “glued together”. 
Figure 2.3.1. A \(P\)SET card
Activity 2.3.1.
Verify that the following are \(\mathbb{P}\)SETs.
(a)
(b)
Activity 2.3.2.
(a)
What \(\mathbb{P}\)SETs can you find here? 
Figure 2.3.3. 12 SET cards.
Activity 2.3.3.
Play \(\mathbb{P}\)SET!
Activity 2.3.4.
(a)
What card(s) can you add to form a \(\mathbb{P}\)SET? 
(b)
Out of these cards, how many \(\mathbb{P}\)SETs can you find?
(c)
Pick any two cards, can you find what card(s) if any will complete a set? How many \(\mathbb{P}\)SETs can you find? Repeat.
Remark 2.3.4.
We will let a \(\mathbb{P}\)line in the \(\mathbb{P}\)SET context to be a collection of 4 cards so that every 3 card subset forms a \(\mathbb{P}\)SET.
Activity 2.3.5.
(a)
Pick any three cards who do not form a \(\mathbb{P}\)SET and arrange them in a corner of the \(3\times 3\) grid:
(b)
Fill out this grid so that each line forms a \(\mathbb{P}\)line.
(c)
For each pair of cards on this grid, do they lie on exactly one \(\mathbb{P}\)line?
