This is a problem involving set theory and Venn diagrams. Let’s break it down step-by-step and solve the two parts of the question.

We are given the following data:

• Total number of persons surveyed = 100.
• $n(A) = 28$ (number of people who read magazine A).
• $n(B) = 30$ (number of people who read magazine B).
• $n(C) = 42$ (number of people who read magazine C).
• $n(A \cap B) = 8$ (number of people who read both magazines A and B).
• $n(A \cap C) = 10$ (number of people who read both magazines A and C).
• $n(B \cap C) = 5$ (number of people who read both magazines B and C).
• $n(A \cap B \cap C) = 3$ (number of people who read all three magazines).

We are to find:
(i) The number of people who read none of the three magazines.
(ii) The number of people who read only magazine C.

Step 1: Using the inclusion-exclusion principle for sets

The inclusion-exclusion formula for three sets is:
$n(A \cup B \cup C) = n(A) + n(B) + n(C) - n(A \cap B) - n(A \cap C) - n(B \cap C) + n(A \cap B \cap C)$
Substitute the values into the formula:
$n(A \cup B \cup C) = 28 + 30 + 42 - 8 - 10 - 5 + 3$
$n(A \cup B \cup C) = 80$
So, 80 people read at least one of the magazines.

Step 2: Number of people who read none of the magazines

The total number of people surveyed is 100. Therefore, the number of people who read none of the magazines is:
$100 - n(A \cup B \cup C) = 100 - 80 = 20$

Thus, 20 people read none of the three magazines.

Step 3: Number of people who read only magazine C

To find the number of people who read only magazine C, we calculate as follows:

1. Total number of people who read magazine C is $n(C) = 42$.
2. Subtract the number of people who read both C and A ($n(A \cap C) = 10$), both C and B ($n(B \cap C) = 5$), and all three magazines ($n(A \cap B \cap C) = 3$).

So, the number of people who read only magazine C is:
$n(C \text{ only}) = n(C) - n(A \cap C) - n(B \cap C) + n(A \cap B \cap C)$
Substitute the values:
$n(C \text{ only}) = 42 - 10 - 5 + 3 = 30$

Thus, 30 people read only magazine C.

Final Answers:

(i) The number of people who read none of the three magazines = 20.
(ii) The number of people who read only magazine C = 30.

Would you like to see the Venn diagram representation or further clarification?

Related Questions to Practice:

1. How many people read exactly two magazines?
2. How many people read only magazine A?
3. How many people read only magazine B?
4. How many people read at least two magazines?
5. How many people read all three magazines?

Tip:

When solving problems with overlapping sets, always organize the data systematically and consider drawing a Venn diagram to visualize the relationships.