I need help with a Venn diagram problem for my discrete mathematics class. This is the problem:

After an unremarkable year, everyone has decided to undertake some new activities. We are interested in exploring patterns around what students have done since the start of 2021, considering which of these activities they did at least once. The following data is calculated for 465 students: 220 joined a student club 159 ate at a cafe 208 went to a gym 68 joined a student club and ate at a cafe 126 joined a student club and went to a gym 32 joined a student club, ate at a cafe and went to a gym 101 did not join a student club, eat at a cafe, or go to a gym

a) [2 marks] ? A value needed for the Venn diagram is missing. Explain how to formally find it and calculate the missing value.

b) [3 marks] ? Provide counts for the following. Show the numerical expression using the values from the Venn diagram you used to find your answer: correct answers without expressions will be awarded 0 marks.

i. Did not go to a gym.

ii. Joined a student club but did not eat at a cafe.

iii. Did one only of joined a student club, eat at a cafe or went to a gym.

c) [2 marks] ? Using each club as a set, represent the following using set operators (, , C or '):

i. Did not go to a gym nor eat at a cafe.

ii. Joined a student club and ate at a cafe but did not go to a gym.