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 x F – G + H ÷ K’?

The correct option is Brother's wife.

To determine how E is related to K in the expression ‘E x F – G + H ÷ K’, let us break down the relation step-by-step using the given code language definitions:

1. E x F means ‘E is the wife of F’.
This implies that E is female and F is male (husband of E).

2. F – G means ‘F is the brother of G’.
So, F and G are siblings.

3. G + H means ‘G is the daughter of H’.
Since G is the daughter of H and F is the brother of G, both F and G are children of H.

4. H ÷ K means ‘H is the father of K’.
This means H is the father of K, as well as the father of F and G. Therefore, F, G, and K are siblings (children of H).

Now, let us combine these relationships to find how E is related to K:
- F is the brother of K.
- E is married to F (E is the wife of F).

Therefore, E is the brother's wife of K.