P is the father of R and S is the son of Q and T is the brother of P. If R is…

Concept

In a blood-relation chain every statement is one edge of a family tree, and the relationship word itself fixes a person's gender: father, son and brother mark a male, while sister and wife mark a female. Once the tree is complete, an in-law tie is read across the connecting marriage - a sibling's spouse or a spouse's sibling stands in the same generation, a spouse stands on the direct marital edge, and a child's spouse stands one generation below.

Building the family tree

1. "P is the father of R" fixes P as male and places P one generation above R.

2. "R is the sister of S" fixes R as female and makes R and S children of the same parents, so P is the father of S as well.

3. "S is the son of Q" fixes S as male and places Q one generation above S, so Q is a parent of S.

4. S already has P as his father, so the remaining parent slot is the mother: Q is female and is the wife of P.

5. "T is the brother of P" fixes T as male and places T beside P in P's own generation.

6. Q is therefore the wife of T's brother - one marriage away from T inside the same generation - so Q is the sister-in-law of T.

Comparing with the other relations

• Wife would need Q to be married to T himself, but the marriage in the tree is Q with P, and T is only P's brother.

• Brother-in-law would need the person related to T to be male, whereas Q is the mother of S and therefore female.

• Daughter-in-law would need Q to be the wife of a son of T, whereas Q's husband P stands in T's own generation.

Cross-check

Reading the same marital edge from the other side, T is the brother of Q's husband, which makes T the brother-in-law of Q; the mirrored pair confirms a sibling-in-law link inside one generation rather than a spousal link or a next-generation link.