Define sets and given information.

Let A be the set of attackers, D be the set of defenders, and M be the set of midfielders.
Total players = 20.
Given:
$|A| = 8$
$|D| = 12$
$|M| = 12$
$|A \cap M| = 5$ (attack and midfield)
$|D \cap M| = 6$ (defense and midfield)
$|A \setminus (M \cup D)| = 2$ (only attack)
$|A \cap D \cap M| = 3$ (all three roles)

• Players in all three roles ($A \cap D \cap M$): 3
• Players in attack and midfield only ($A \cap M \setminus D$): $|A \cap M| - |A \cap D \cap M| = 5 - 3 = 2$
• Players in defense and midfield only ($D \cap M \setminus A$): $|D \cap M| - |A \cap D \cap M| = 6 - 3 = 3$
• Players in attack only ($A \setminus (M \cup D)$): 2
• Players in attack and defense only ($A \cap D \setminus M$): The total in A is 8. We have 2 (A only), 2 (A and M only), 3 (all three). So, $|A \cap D \setminus M| = |A| - (|A \setminus (M \cup D)| + |A \cap M \setminus D| + |A \cap D \cap M|)$ $|A \cap D \setminus M| = 8 - (2 + 2 + 3) = 8 - 7 = 1$
• Players in defense only ($D \setminus (A \cup M)$): The total in D is 12. We have 1 (A and D only), 3 (D and M only), 3 (all three). So, $|D \setminus (A \cup M)| = |D| - (|A \cap D \setminus M| + |D \cap M \setminus A| + |A \cap D \cap M|)$ $|D \setminus (A \cup M)| = 12 - (1 + 3 + 3) = 12 - 7 = 5$
• Players in midfield only ($M \setminus (A \cup D)$): The total in M is 12. We have 2 (A and M only), 3 (D and M only), 3 (all three). So, $|M \setminus (A \cup D)| = |M| - (|A \cap M \setminus D| + |D \cap M \setminus A| + |A \cap D \cap M|)$ $|M \setminus (A \cup D)| = 12 - (2 + 3 + 3) = 12 - 8 = 4$

Sum of all distinct regions: $2 (\text{A only}) + 5 (\text{D only}) + 4 (\text{M only}) + 1 (\text{A and D only}) + 2 (\text{A and M only}) + 3 (\text{D and M only}) + 3 (\text{A and D and M}) = 2 + 5 + 4 + 1 + 2 + 3 + 3 = 20$.
This matches the total number of players invited.

i. Illustrate the information in a Venn diagram
A Venn diagram would show three overlapping circles (A, D, M) with the following numbers in each distinct region:

• Only Attack (A only): 2
• Only Defense (D only): 5
• Only Midfield (M only): 4
• Attack and Defense only ($A \cap D \setminus M$): 1
• Attack and Midfield only ($A \cap M \setminus D$): 2
• Defense and Midfield only ($D \cap M \setminus A$): 3
• Attack, Defense, and Midfield ($A \cap D \cap M$): 3

ii. Find the number of players that can play:

a) only midfield
This is the number of players in the "Midfield only" region.
Number of players = 4
The number of players that can play only midfield is $\boxed{\text{4}}$.

b) exactly 2 roles
This is the sum of players in the regions where exactly two sets overlap:
(Attack and Defense only) + (Attack and Midfield only) + (Defense and Midfield only)
Number of players = $1 + 2 + 3 = 6$
The number of players that can play exactly 2 roles is $\boxed{\text{6}}$.