1. **Problem statement:** Find the value of $x$, the number of students who enjoy none of the activities (running, cycling, swimming) given the Venn diagram data and total students $100$. 2. **Given data from the Venn diagram:** - Only Running (R) = 25 - Only Cycling (C) = 21 - Only Swimming (S) = 13 - Running and Cycling only = 7 - Running and Swimming only = 4 - Cycling and Swimming only = 2 - All three (R \cap C \cap S) = 5 - None = $x$ 3. **Formula:** Total students = Sum of all disjoint regions in the Venn diagram + those who enjoy none $$100 = 25 + 21 + 13 + 7 + 4 + 2 + 5 + x$$ 4. **Calculate sum of known values:** $$25 + 21 = 46$$ $$46 + 13 = 59$$ $$59 + 7 = 66$$ $$66 + 4 = 70$$ $$70 + 2 = 72$$ $$72 + 5 = 77$$ 5. **Find $x$:** $$100 = 77 + x$$ $$x = 100 - 77$$ $$x = 23$$ **Final answer:** $$\boxed{23}$$ students enjoy none of the activities.