In the code below, “+” means “is the brother of”, “−” means “is the wife of”, and “*” means “is the mother of”. Which expression correctly represents “M is the brother-in-law of P”?

Introduction / Context:
Coded relations replace kinship words with symbols, and the job is to compose the correct chain that matches the target relationship. Here, “+” is brother-of, “−” is wife-of, and “*” is mother-of. We seek an expression meaning “M is the brother-in-law of P,” i.e., M is either (1) the brother of P’s spouse, or (2) the husband of P’s sister. We will test each option against the symbol legend and semantics.

Given Data / Assumptions:

• A + B → A is the brother of B (A is male).
• A − B → A is the wife of B (A is female).
• A * B → A is the mother of B (A is female).
• “Brother-in-law of P” requires M to be male and related via spouse’s sibling or sibling’s spouse.

Concept / Approach:
Translate each candidate string from left to right into words and see if it implies “M is P’s brother-in-law.” Watch out for gender mismatches: “wife-of” and “mother-of” force the subject to be female, which cannot describe M if M must be a brother-in-law (male).

Step-by-Step Solution:

Verification / Alternative check:
The only path that creates “brother of P’s spouse” with M male is option (b). The other patterns either force M to be female or break the intended in-law link.

Why Other Options Are Wrong:

• (a), (c), (d) set M or P genders inconsistently with “brother-in-law.”
• None of these is unnecessary because (b) already satisfies the requirement.

Common Pitfalls:

• Reading from right to left; here the natural read is left to right.
• Overlooking the gender constraints implied by “wife” and “mother.”

Final Answer:

M + N - P