In a group of 15 people; 7 can read French, 8 can read English while 3 of them can read neither of these two languages. The number of people who can read exactly one language is

The correct option is 9.

Step-by-step Explanation:

Let us define the sets for the given problem:
Let $U$ represent the universal set of all people in the group.
Let $F$ represent the set of people who can read French.
Let $E$ represent the set of people who can read English.

From the problem, we are given the following values:

$\left|U\right|=15$

$\left|F\right|=7$

$\left|E\right|=8$

We are also told that 3 people can read neither of these two languages. This means these 3 people lie outside the union of set $F$ and set $E$.
Thus, the number of people who can read at least one of the two languages is:

$|F\cup E|=\left|U\right|-3=15-3=12$

Next, we use the principle of inclusion-exclusion to find the number of people who can read both languages:

$|F\cup E|=\left|F\right|+\left|E\right|-|F\cap E|$

Substitute the known values into the equation:

$12=7+8-|F\cap E|$

$12=15-|F\cap E|$

$|F\cap E|=15-12=3$

This tells us that 3 people can read both French and English.

To find the number of people who can read exactly one language, we subtract the number of people who read both languages from the total number of people who read at least one language:

$\text{People reading exactly one language}=|F\cup E|-|F\cap E|$

$\text{People reading exactly one language}=12-3=9$

Thus, the number of people who can read exactly one language is 9.