The problem asks us to choose the Venn diagram that correctly illustrates the following two statements: P: All students offering Literature (L) also offer History (H). Q: Students offering History (H) do not offer Geography (G).

1. Problem Description

The problem asks us to choose the Venn diagram that correctly illustrates the following two statements:

P: All students offering Literature (L) also offer History (H).

Q: Students offering History (H) do not offer Geography (G).

2. Solution Steps

Statement P: "All students offering Literature (L) also offer History (H)" implies that the set L is a subset of the set H. In other words, L must be entirely contained within H. Mathematically, $L \subseteq H$.

Statement Q: "Students offering History (H) do not offer Geography (G)" implies that there is no overlap between the set H and the set G. In other words, the intersection of H and G is the empty set. Mathematically, $H \cap G = \emptyset$.

Now we analyze each option:

A. In this diagram, L, H, and G all intersect. In particular, H and G intersect, which violates statement Q. Also, L is not entirely contained within H, violating statement P.

B. In this diagram, G and H are separate, so $G \cap H = \emptyset$. Also, H contains L, so $L \subseteq H$. Both statements P and Q are satisfied.

C. In this diagram, G and H are separate, so $G \cap H = \emptyset$. However, L is inside H, but H does not entirely contain L. This is a contradiction since L contains H, implying all H offer L, where the question statement is that all L offer H. This is not the correct implication.

D. In this diagram, H and G intersect, violating statement Q.

3. Final Answer

B