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34 students are asked which of the sporting activities sprint, long jump or high jump they practice. The replies showed that 16 do not practice sprint, 17 do not practice long jump, and 22 do not practice high jump. 7 students practice sprint only, 6 students practice high jump only and 7 students practice long jump only. of those who practice only two of the sporting activities 2 do not practice long jump. Draw a Venn diagram to illustrate this information. Determine the number of students who do not practice any of the sporting activities. Find the number of students who practice all the three sporting activities​

Sagot :

Nottheleaf

Réponse:

To draw the Venn diagram:

Let's represent the sets as follows:

- S: Sprint

- L: Long jump

- H: High jump

Using the information provided:

- 7 students practice sprint only (S)

- 7 students practice long jump only (L)

- 6 students practice high jump only (H)

- 2 students practice both sprint and long jump (S ∩ L)

- 16 students do not practice sprint (S')

- 17 students do not practice long jump (L')

- 22 students do not practice high jump (H')

We can fill in the Venn diagram accordingly:

```

S

/ \

/ \

/ L \

H-----S'L'

\ /

\ /

\ /

H'

```

To find the number of students who do not practice any of the sporting activities:

- Count the students outside all circles: \(S' \cap L' \cap H' = 2\)

So, 2 students do not practice any of the sporting activities.

To find the number of students who practice all three sporting activities:

- Since 2 students do not practice long jump among those who practice only two activities, the students who practice all three sports are in \(L \cap H \cap S\).

- We know that \(S = 7 + 2 = 9\) (Sprint)

- \(L = 7 + 2 = 9\) (Long jump)

- \(H = 6 + 2 = 8\) (High jump)

Since \(S = 9\), \(L = 9\), and \(H = 8\), and these numbers should sum up to the total number of students (34), we can calculate the number of students who practice all three sports:

\(7 + 2 + 6 + 2 + 7 + 2 + 7 + 6 + 8 + 2 = 49\)

So, 49 students practice all three sporting activities.

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