Let's solve this problem step by step using the given information. We are dealing with sets and their intersections, so we'll use Venn diagrams or set notation to organize the information.

Given Data:

• Total number of students = 100
• Number of students studying C = 65
• Number of students studying C++ = 45
• Number of students studying Python = 42
• Number of students studying both C and C++ = 20
• Number of students studying both C and Python = 25
• Number of students studying both C++ and Python = 15
• The number of students studying all three languages (C, C++, and Python) is unknown (denote it by $x$).

We need to find the number of students studying:

1. Only C and C++ (not Python)
2. Only C and Python (not C++)

Step 1: Define Sets

Let:

• $C$ represent the set of students studying C.
• $C++$ represent the set of students studying C++.
• $P$ represent the set of students studying Python.

We'll use the following notation:

• $|A \cap B|$ represents the number of students studying both $A$ and $B$.
• $|A \cap B \cap C|$ represents the number of students studying all three languages.

Step 2: Use Set Formulas to Organize Information

The formula for the total number of students studying any of the languages is:

$|C \cup C++ \cup P| = |C| + |C++| + |P| - |C \cap C++| - |C \cap P| - |C++ \cap P| + |C \cap C++ \cap P|$

Substitute the values we know:

$100 = 65 + 45 + 42 - 20 - 25 - 15 + x$

Simplifying this:

$100 = 152 - 60 + x$ $100 = 92 + x$ $x = 8$

So, 8 students are studying all three languages (C, C++, and Python).

Step 3: Find the Number of Students for Each Part

(i) Only C and C++ (not Python)

The number of students studying only C and C++ but not Python is:

$|C \cap C++| - |C \cap C++ \cap P| = 20 - 8 = 12$

(ii) Only C and Python (not C++)

The number of students studying only C and Python but not C++ is:

$|C \cap P| - |C \cap C++ \cap P| = 25 - 8 = 17$

Final Answer:

1. The number of students studying only C and C++ (not Python) is 12.
2. The number of students studying only C and Python (not C++) is 17.

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Do you want further details or have any questions? Here are some related questions you can explore:

1. How many students study all three languages?
2. How many students study only Python?
3. How many students study only C++?
4. What is the total number of students studying two or more languages?
5. How many students study neither Python nor C++?

Tip: When solving problems involving sets and intersections, using a Venn diagram can help visually organize the relationships between the sets.