math: 38 learners at a high school,24play hockey,30play netball and 4play neither hockey nor netball.use venn diagram

How many play both? If x, then

24+30-x = 38-4
x = 20
So,
4 play only hockey
10 play only netball
20 play both

To solve this problem using a Venn diagram, follow these steps:

Step 1: Draw a rectangle to represent the 38 learners in the high school.

Step 2: Inside the rectangle, draw two overlapping circles. Label one circle as "Hockey" and the other as "Netball."

Step 3: Write the given numbers in the appropriate regions of the Venn diagram. In this case, we know that 24 learners play hockey, 30 play netball, and 4 play neither.

Step 4: Place the number 24 in the region that represents the intersection between the Hockey and Netball circles. This shows that 24 learners play both hockey and netball.

Step 5: Place the number 4 outside the circles but inside the rectangle to represent the learners who play neither hockey nor netball.

Step 6: Fill in the remaining regions. Since the total number of learners is 38, we need to calculate how many learners play only hockey and how many play only netball. To do this, subtract the number of learners who play both (24) from the total number of learners who play hockey and netball combined(30). So, there are 30 - 24 = 6 learners who play only netball. And since 24 learners play hockey, there are 24 - 6 = 18 learners who play only hockey.

Here's how the Venn diagram should look:

_____38_____
/ \
/ \
/ \
18 6 24
HOCKEY (both) NETBALL
\ /
\ /
\_____4_____/