Answer:
2.3.2 To find the number of youths who jog but do not swim or cycle, we need to find the number of elements in the jog set that do not intersect with either swim or cycle. From the diagram, this would be (Jog - Jog ∩ Swim - Jog ∩ Cycle + Jog ∩ Swim ∩ Cycle). So, 50 - 14 - 9 + 3 = 30 youths jog but do not swim or cycle.2.3.3 To find the number of youths who take part in only one of the three activities, we sum the number of elements in each individual set (Jog, Swim, Cycle) and subtract the overlaps (Jog ∩ Swim + Jog ∩ Cycle + Swim ∩ Cycle) and then subtract the triple overlap (Jog ∩ Swim ∩ Cycle). So, (50 + 30 + 35 - 14 - 7 - 9) - 3 = 82 youths take part in only one of the three activities.2.3.4 To find the number of youths who do not take part in any of the three activities, we subtract the total number of youths from the sum of those who take part in at least one activity. So, 100 - (50 + 30 + 35 - 14 - 7 - 9 + 3) = 18 youths do not take part in any of the three activities.
2.3.1 Venn diagram:
2.3.2 Number of youths that jog but do not swim or cycle = (Number of youths that jog) - (Number of youths that jog and swim) - (Number of youths that jog and cycle) + (Number of youths that jog, swim and cycle)
= 50 - 14 - 9 + 3
= 30 youths jog but do not swim or cycle.
2.3.3 Number of youths who take part in only one of the three activities = (Number of youths that jog but do not swim or cycle) + (Number of youths that swim but do not jog or cycle) + (Number of youths that cycle but do not jog or swim)
= 30 + 16 + 19
= 65 youths take part in only one of the three activities.
2.3.4 Number of youths who do not take part in any of the three activities = Total number of youths - (Number of youths that jog) - (Number of youths that swim) - (Number of youths that cycle) + (Number of youths that jog, swim, and cycle)
= 100 - 50 - 30 - 35 + 3
= 18 youths do not take part in any of the three activities.
