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.

Step 1: Find the symmetric difference A B. The symmetric difference A 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 B = \1, 2, 3, 4, 5, 6, 8, 9\ Next, find the intersection of A and B: A B = \5, 8\ Now, find the symmetric difference: A B = (A B) (A B) A B = \1, 2, 3, 4, 5, 6, 8, 9\ \5, 8\ A B = \1, 2, 3, 4, 6, 9\ The symmetric difference is \1, 2, 3, 4, 6, 9\. Step 2: Interpret the Venn diagram for question 1b. 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: 7 ii) only football: 14 iii) only hockey: 8 iv) all the three games: 16 v) hockey and football but not cricket: 11 vi) cricket and football but not hockey: 5 vii) cricket and hockey but not football: 4 viii) non of the three games: Information not provided in the diagram. Send me the next one 📸