The problem consists of two parts. (i) We are asked to illustrate the statement "All good Literature students in a school are in the General Arts class" using a Venn diagram. (ii) We are then asked to use the diagram to determine whether the three given conclusions are valid based on the initial statement.

1. Problem Description

The problem consists of two parts.

(i) We are asked to illustrate the statement "All good Literature students in a school are in the General Arts class" using a Venn diagram.

(ii) We are then asked to use the diagram to determine whether the three given conclusions are valid based on the initial statement.

2. Solution Steps

(i) Venn Diagram Representation:

Let $L$ be the set of all good Literature students.

Let $G$ be the set of all students in the General Arts class.

The statement "All good Literature students in a school are in the General Arts class" means that $L$ is a subset of $G$, i.e., $L \subseteq G$. In a Venn diagram, this is represented by a circle for $L$ being completely contained within a circle for $G$.

(ii) Validity of Conclusions:

I. "Vivian is in the General Arts class therefore she is a good Literature student."

This is equivalent to saying if Vivian $\in G$, then Vivian $\in L$. However, since $L \subseteq G$, being in $G$ does not guarantee being in $L$. There might be students in $G$ who are not in $L$. Therefore, this conclusion is invalid.

II. "Audu is not a good Literature student therefore he is not in the General Arts class."

This is equivalent to saying if Audu $\notin L$, then Audu $\notin G$. Since $L \subseteq G$, if Audu is not in $L$, he could still be in $G \setminus L$. For example, Audu could be a student in the General Arts class but not a good Literature student. Therefore, this conclusion is invalid. The valid conclusion would be if Audu is not in the General Arts class, then he is not a good Literature student.

III. "Kweku is not in the General Arts class therefore he is not a good Literature student."

This is equivalent to saying if Kweku $\notin G$, then Kweku $\notin L$. Since $L \subseteq G$, if Kweku is outside of $G$, he must also be outside of $L$. Thus, this conclusion is valid.

3. Final Answer

(i) The Venn diagram should show a circle representing "good Literature students" contained entirely within a larger circle representing "General Arts class students".

(ii)

I. Invalid.

II. Invalid.

III. Valid.