In a certain code language, ‘A + B’ means ‘A is the son of B’, ‘A − B’ means…

In a coded blood-relation question, first decode every symbol into its literal family relation using the given key. Then read the expression left to right as a chain of consecutive pairs, converting each pair into one directed family link (parent, child, sibling, or spouse). Once all the links are known, redraw them as a small family tree and read off the relation between the two named people by combining standard kinship terms (for example, father's father = grandfather, brother's wife = sister-in-law) rather than guessing directly from the symbols. A phrasing rule decides the direction of the whole answer: ‘How is X related to Y?’ always asks for X’s relation to Y, i.e. it is answered by completing the sentence ‘X is Y’s ___’. So the chain of links is traced starting at Y and ending at X, never the other way round.

1. Decode the key: '+' = son of, '−' = brother of, '×' = wife of, '÷' = father of.

2. Split the expression 'D + F ÷ G × H − J' into consecutive pairs: D+F, F÷G, G×H, H−J.

3. D + F: D is the son of F, so F is D's parent (D is male, so D is F's son).

4. F ÷ G: F is the father of G, so F is also G's parent — D and G share the same parent F, making D and G siblings; since D is male, D is G's brother.

5. G × H: G is the wife of H, so G is married to H.

6. H − J: H is the brother of J, so H and J are siblings, with H male.

7. Combine the links from J's side: J's brother is H; H's wife is G; G's brother is D. So D is linked to J as J's brother's wife's brother.

Cross-check by re-tracing from J: J's sibling is H (from H − J); H's spouse is G (from G × H); G's sibling is D, since D and G share the same father F (from D + F and F ÷ G). The chain J → brother (H) → wife (G) → brother (D) reproduces the same path, confirming the link is consistent.

Note the direction once more: the question asks how D is related to J, so the answer completes ‘D is J’s ___’ and the trace runs from J outwards to D. Reading the very same links in the opposite direction would answer a different question — how J is related to D — for which J would be D’s sister’s husband’s sibling (G is D’s sister, H is G’s husband, J is H’s sibling). Be careful with gender here: ‘H is the brother of J’ fixes H as male but says nothing about J, so J’s own gender is never determined by the expression. That reversed question is not what is asked.

Therefore, D is related to J as J's brother's wife's brother.