If "A $ B" means "A is brother of B", "A @ B" means "A is wife of B", "A # B" means "A is daughter of B" and "A & B" means "A is father of B", which of the following expressions indicates that K is father-in-law of H?

Introduction / Context:
Symbol based blood relation questions replace words like brother, wife, daughter and father with special symbols. You must decode each expression step by step and then check which one satisfies a target relation. Here, the target is that K should be the father-in-law of H.

Given Data / Assumptions:

• A $ B means A is brother of B.
• A @ B means A is wife of B.
• A # B means A is daughter of B.
• A & B means A is father of B.
• We need an expression in terms of H, J, L, P and K such that K becomes father-in-law of H.
• Father-in-law of H means K is the father of the spouse of H.

Concept / Approach:
The best approach is to take each option separately and translate the symbols into words from left to right. Once the full set of relations is known, we see whose father K is and who H is married to. When we find an option where K is the father of H spouse, we have the correct expression.

Step-by-Step Solution (for the correct option c):
Step 1: Consider option c: H @ J $ L # K & P.Step 2: Decode "H @ J": H is wife of J. So J is the husband of H.Step 3: Decode "J $ L": J is brother of L. So J and L are siblings and J is male.Step 4: Decode "L # K": L is daughter of K. So K is a parent of L, and L is female.Step 5: Decode "K & P": K is father of P, so K is definitely male and parent of P.Step 6: From steps 3 and 4, J is the brother of L and L is child of K. Under ordinary assumptions, if L is a child of K and J is her brother, then J is also a child of K. Therefore K is the father of J.Step 7: Because H is the wife of J and K is the father of J, K is the father-in-law of H.

Verification / Alternative check for other options:
In option a, after decoding, K turns out to be a sibling of J rather than the parent of J, so K becomes a brother-in-law, not father-in-law. In option b, K appears as a parent of L in a way that does not make L sibling of J in the correct generation for J to be H spouse child of K. In option d, the structure makes K parent of L, who is child of J, but H is wife of P, so K relates to the wrong branch. Option e also fails when fully decoded, because K is not the father of H spouse.

Why Other Options Are Wrong:
Each incorrect choice either makes K the brother of someone, the spouse of someone or the parent of the wrong person, rather than the father of the person married to H. Only in option c does K end up being the father of J, and J is clearly shown as the husband of H, which matches exactly the definition of father-in-law.

Common Pitfalls:
Candidates often try to mentally decode all symbols at once and become confused. A better approach is to read each symbol pair slowly and write small notes like "H wife of J", "J brother of L" and so on. Also, do not assume symmetry of the relations when they are not symmetric by definition. For example, "A @ B" only tells you that A is wife of B, and from that you must deduce B is husband of A, but the roles remain distinct.

Final Answer:
The expression that correctly shows K as father-in-law of H is H @ J $ L # K & P.