Find the symmetric difference of sets A = 1, 2, 4, 5, 8 and B = 3, 5, 6, 8, 9. Also, interpret a Venn diagram for a problem involving students playing cricket, hockey, and football.

The symmetric difference $A \Delta B$ is defined as the set of elements that are in either set A or set B, but not in their intersection.
Given sets:
$A = \{1, 2, 4, 5, 8\}$
$B = \{3, 5, 6, 8, 9\}$

First, find the union of A and B:

$$A \cup B = \{1, 2, 3, 4, 5, 6, 8, 9\}$$

Next, find the intersection of A and B:

$$A \cap B = \{5, 8\}$$

Now, find the symmetric difference:

$$A \Delta B = (A \cup B) \setminus (A \cap B)$$ $$A \Delta B = \{1, 2, 3, 4, 5, 6, 8, 9\} \setminus \{5, 8\}$$ $$A \Delta B = \{1, 2, 3, 4, 6, 9\}$$

The symmetric difference is $\boxed{\{1, 2, 3, 4, 6, 9\}}$.

The Venn diagram shows the number of students playing Cricket, Hockey, and Football.

a) Number of students who played only cricket:
This is the region within the Cricket circle that does not overlap with Hockey or Football.
Number of students = 7

b) Number of students who played only football:
This is the region within the Football circle that does not overlap with Cricket or Hockey.
Number of students = 14

c) Number of students who played only hockey:
This is the region within the Hockey circle that does not overlap with Cricket or Football.
Number of students = 8

d) Number of students who played all three games:
This is the region where all three circles (Cricket, Hockey, Football) overlap.
Number of students = 16

e) Number of students who played hockey and football but not cricket:
This is the region where the Hockey and Football circles overlap, but outside the Cricket circle.
Number of students = 11

f) Number of students who played cricket and football but not hockey:
This is the region where the Cricket and Football circles overlap, but outside the Hockey circle.
Number of students = 5

g) Number of students who played cricket and hockey but not football:
This is the region where the Cricket and Hockey circles overlap, but outside the Football circle.
Number of students = 4

h) Number of students who played none of the three games:
This information is not provided in the given Venn diagram. The number of students outside all three circles is not specified.

Here are the answers for 1b:

i) only cricket: $\boxed{7}$

ii) only football: $\boxed{14}$

iii) only hockey: $\boxed{8}$

iv) all the three games: $\boxed{16}$

v) hockey and football but not cricket: $\boxed{11}$

vi) cricket and football but not hockey: $\boxed{5}$

vii) cricket and hockey but not football: $\boxed{4}$

viii) non of the three games: Information not provided in the diagram.