In a certain code language,
A + B means ‘A is the daughter of B’
A – B means ‘A is the brother of B’
A x B means ‘A is the wife of B’
A ÷ B means ‘A is the father of B’
Based on the above, how is E related to K if ‘E – F + G ÷ H x K’?

The correct option is Wife's brother.

To understand why this is correct, we can decode the relation expression E – F + G ÷ H x K step-by-step from left to right using the given coded definitions:

1. E – F:
According to the code, 'A – B' means 'A is the brother of B'. Therefore, E is the brother of F. This tells us E is male, and E and F are siblings.

2. F + G:
According to the code, 'A + B' means 'A is the daughter of B'. Therefore, F is the daughter of G. Since E and F are siblings, this indicates G is the parent of both E and F (making E the son of G).

3. G ÷ H:
According to the code, 'A ÷ B' means 'A is the father of B'. Therefore, G is the father of H. Since G is the father of both E and F as well, E, F, and H are all siblings sharing the same father, G. This means E is the brother of H.

4. H x K:
According to the code, 'A x B' means 'A is the wife of B'. Therefore, H is the wife of K. This establishes that K is H's husband, or conversely, H is K's wife.

Combining these pieces of information:
- K's wife is H.
- E is the brother of H.
- Consequently, E is K's wife's brother.