Let U be the universal set. If n(C \ W) = 20%, n(W \ C) = 65%, and n((C U W)') = 5%, find n(C U W) and represent the information in a Venn diagram.

Here's the solution to question 6. b):

Let $U$ be the set of all people surveyed (representing 100%).
Let $C$ be the set of people using cellular data.
Let $W$ be the set of people using Wi-Fi.

Given information in percentages:
People using cellular data but not Wi-Fi: $n(C \setminus W) = 20\%$
People using Wi-Fi but not cellular data: $n(W \setminus C) = 65\%$
People using neither cellular data nor Wi-Fi: $n(C \cup W)' = 5\%$

Step 1: Calculate the percentage of people using both cellular data and Wi-Fi.
The sum of all disjoint regions must equal 100%:

$$n(U) = n(C \setminus W) + n(W \setminus C) + n(C \cap W) + n(C \cup W)'$$ $$100\% = 20\% + 65\% + n(C \cap W) + 5\%$$ $$100\% = 90\% + n(C \cap W)$$ $$n(C \cap W) = 100\% - 90\%$$ $$n(C \cap W) = 10\%$$

b) (i) If C and W denote the sets of people who are using cellular data and Wi-Fi respectively, write the cardinality of $n(C \cup W)$.
The cardinality of $n(C \cup W)$ is the percentage of people using at least one of the services.

$$n(C \cup W) = n(C \setminus W) + n(W \setminus C) + n(C \cap W)$$ $$n(C \cup W) = 20\% + 65\% + 10\%$$ $$n(C \cup W) = 95\%$$

The cardinality of $n(C \cup W)$ is $\boxed{95\%}$.

b) (ii) Represent the above information in a Venn-diagram.
A Venn diagram would illustrate:

• A rectangle representing the universal set $U$ (100%).
• Two overlapping circles, one labeled $C$ and one labeled $W$.
• The region for $C$ only ($C \setminus W$) contains 20%.
• The region for $W$ only ($W \setminus C$) contains 65%.
• The intersection region ($C \cap W$) contains 10%.
• The region outside both circles ($(C \cup W)'$) contains 5%.

b) (iii) Find the percent of people who are using Wi-Fi.
The percent of people using Wi-Fi is the sum of those using Wi-Fi only and those using both:

$$n(W) = n(W \setminus C) + n(C \cap W)$$ $$n(W) = 65\% + 10\%$$ $$n(W) = 75\%$$

The percent of people using Wi-Fi is $\boxed{75\%}$.

b) (iv) By what percent of the people who are not using cellular data is more or less than the people who are not using Wi-Fi?
First, find the percent of people who are not using cellular data ($n(C')$):

$$n(C') = n(W \setminus C) + n(C \cup W)'$$ $$n(C') = 65\% + 5\%$$ $$n(C') = 70\%$$

Next, find the percent of people who are not using Wi-Fi ($n(W')$):

$$n(W') = n(C \setminus W) + n(C \cup W)'$$ $$n(W') = 20\% + 5\%$$ $$n(W') = 25\%$$

Now, find the difference:

$$n(C') - n(W') = 70\% - 25\%$$ $$n(C') - n(W') = 45\%$$

Since the result is positive, the percentage of people not using cellular data is 45% more than the percentage of people not using Wi-Fi.
It is \boxed{\text{45% more}}.