there is 25kids. 12 likes math, 15 natural sciences and 6 both. How mutch doesnt like math and natural sciences

We can solve this problem using a set theory approach with the following steps:

### Step 1: Identify the sets
- \( |M| = 12 \) (kids who like math),
- \( |N| = 15 \) (kids who like natural sciences),
- \( |M \cap N| = 6 \) (kids who like both math and natural sciences).

### Step 2: Use the inclusion-exclusion principle
To find how many kids like either math or natural sciences (or both), we use the inclusion-exclusion principle:

\[
|M \cup N| = |M| + |N| - |M \cap N|
\]
\[
|M \cup N| = 12 + 15 - 6 = 21
\]

So, 21 kids like either math, natural sciences, or both.

### Step 3: Find how many kids don't like either subject
The total number of kids is 25, and 21 kids like math or natural sciences. Therefore, the number of kids who don't like either subject is:

\[
25 - 21 = 4
\]

### Conclusion:
4 kids don't like either math or natural sciences.

Would you like more details on any step, or have any questions?

Here are 5 related questions for practice:
1. How many kids like only math?
2. How many kids like only natural sciences?
3. What percentage of the kids like both subjects?
4. What percentage of the kids like neither subject?
5. How would the result change if 10 kids liked both subjects?

**Tip:** The inclusion-exclusion principle is handy when dealing with overlapping groups!

There are 25 kids. 12 like math, 15 like natural sciences, and 6 like both. How many don't like math or natural sciences?

Learn how to solve a set theory problem where 25 kids like math or natural sciences. Use the inclusion-exclusion principle to find how many kids don't like either subject. Suitable for students in Grades 5-7.

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