1.A3P means A is the mother of P . 2.A4P means A is the brother of P. 3.A9P…

Concept: In coded family-relation puzzles, each digit stands for a fixed relation (3 = mother of, 4 = brother of, 9 = husband of, 5 = daughter of). Decode the chain of codes to build a partial family tree, then combine gender and generation to name the compound relationship being asked about. A mother-in-law is specifically the mother of one's spouse — female, one generation above, linked through marriage.

1. M9N → M is the husband of N, so M and N are a married couple.

2. N5K → N is the daughter of K, so K is a parent of N — that is, a parent of M's wife.

3. K3J → K is the mother of J, which confirms K is female.

4. A female parent of one's spouse is exactly a mother-in-law, so K is the mother-in-law of M.

Cross-check: Being a mother-in-law needs both conditions together — female, and a parent of the spouse. K3J supplies the gender (K is a mother), and N5K plus M9N supply the relation (K is the parent of M's wife N). Both hold together only for this coding; in the other option strings K instead comes out as M's own child, as the mother-in-law of a different person, or unrelated to M by generation or marriage, so neither condition is jointly satisfied there.