Question

65 people were asked on the activities they engage in during their free time. The results showed that 23 visit national parks, 26 engage in cycling while 22 engage in swimming. Furthermore 9 engage in swimming and visit national parks, 9 engage in swimming only while 11 visit national parks only. How many engage in a) Swimming and cycling b) Cycling only c) Neither swimming nor visiting national parks nor cycling

Answer 1

Using a Venn diagram, we can determine that 14 people engage in swimming and cycling, 17 people engage in cycling only, and no one falls into the category of neither swimming nor visiting national parks nor cycling.

Step-by-step explanation:

To solve this problem, we can use a Venn diagram. Let's define the following sets:

S = Set of people who engage in swimming

C = Set of people who engage in cycling

N = Set of people who visit national parks

From the given information, we know that:

|N| = 23, |C| = 26, |S| = 22

|S ∩ N| = 9, |S - N| = 9, |N - S| = 11

We can start by filling in the values we know:

• |S ∩ N| = 9
• |S - N| = 9
• |N - S| = 11

Next, we can use this information to fill in the remaining values:

• |S ∪ N| = |S ∩ N| + |S - N| + |N - S|
• |S ∪ N| = 9 + 9 + 11
• |S ∪ N| = 29
• |C - S| = |C| - |C ∩ S|
• |C - S| = 26 - |S ∩ C|
• |C - S| = 26 - |S ∩ N|
• |C - S| = 26 - 9
• |C - S| = 17
• |C ∪ N| = |C| + |N| - |C ∩ N|
• |C ∪ N| = 26 + 23 - |S ∩ N|
• |C ∪ N| = 26 + 23 - 9
• |C ∪ N| = 40

So, the final answers are:

• a) Swimming and cycling: |S ∩ C| = |C ∪ N| - |C| = 40 - 26 = 14
• b) Cycling only: |C - S| = 17
• c) Neither swimming nor visiting national parks nor cycling: Total number of people - (|S ∪ N| + |S - N| + |N - S| + |C ∪ N| + |C - S|) = 65 - (29 + 9 + 11 + 40 + 17) = 65 - 106 = 0 (There are no people in this category)

Answer 2

a)=57

b)=26

C)= 35

Step-by-step explanation:

there is 100 people recorded when they only wanted 65 so the 35 extra answers are not recorded.