Decoding Symbolic Relationships: Finding the Paternal Uncle

This question asks us to identify a specific family relationship using a set of defined symbols. We are given three rules:

• $A \text{ -- } B$ means that A is the brother of B.
• $A + B$ means that A is the sister of B.
• $A \div B$ means that A is the father of B.

We need to find which expression shows that P is the paternal uncle of R. A paternal uncle is the brother of one's father. Therefore, we are looking for an expression where P is the brother of R's father.

Let's break down what "P is the paternal uncle of R" means using the given symbols. It means:

1. There is someone who is the father of R. Let's call this person X. According to the rules, this is represented as $X \div R$.
2. P is the brother of this person X. According to the rules, this is represented as $P \text{ -- } X$.

Combining these two parts, the relationship we are looking for is represented by an expression like $P \text{ -- } X \div R$. We need to examine the given options to see which one matches this structure, where X is represented by the intermediate variable (Q in the options).

Analyzing Each Relationship Expression Option

Let's examine each option provided and determine the relationship between P and R:

Option 1: $P + Q \div R$

• First, consider $Q \div R$. According to the rule, this means Q is the father of R.
• Next, consider $P + Q$. According to the rule, this means P is the sister of Q.
• So, P is the sister of Q, and Q is the father of R. This means P is the sister of R's father. This relationship is R's paternal aunt.

This option does not show P as the paternal uncle of R.

Option 2: $P \div Q \text{ -- } R$

• First, consider $Q \text{ -- } R$. According to the rule, this means Q is the brother of R.
• Next, consider $P \div Q$. According to the rule, this means P is the father of Q.
• So, P is the father of Q, and Q is the brother of R. This means P is the father of R's brother. This relationship is R's father.

This option does not show P as the paternal uncle of R.

Option 3: $P \text{ -- } Q \div R$

• First, consider $Q \div R$. According to the rule, this means Q is the father of R.
• Next, consider $P \text{ -- } Q$. According to the rule, this means P is the brother of Q.
• So, P is the brother of Q, and Q is the father of R. This means P is the brother of R's father. This relationship is R's paternal uncle.

This option shows P as the paternal uncle of R, which is the relationship we are looking for.

Option 4: $P \text{ -- } Q + R$

• First, consider $Q + R$. According to the rule, this means Q is the sister of R.
• Next, consider $P \text{ -- } Q$. According to the rule, this means P is the brother of Q.
• So, P is the brother of Q, and Q is the sister of R. This means P is the brother of R's sister. This relationship is R's brother.

This option does not show P as the paternal uncle of R.

Conclusion on Paternal Uncle Relationship

Based on the analysis of each option, the expression $P \text{ -- } Q \div R$ correctly represents the relationship where P is the paternal uncle of R. This is because $Q \div R$ establishes Q as the father of R, and $P \text{ -- } Q$ establishes P as the brother of Q (R's father), making P the paternal uncle of R.

Revision Table: Symbolic Relationships

Additional Information on Blood Relations Logic

Problems involving symbolic blood relations require careful step-by-step analysis. Here are some tips for solving such logic puzzles:

• Understand the Symbols: Clearly define what each symbol represents in terms of family relationships (e.g., brother, sister, father, mother, son, daughter, etc.).
• Break Down the Expression: For a complex expression like $P \text{ -- } Q \div R$, analyze it part by part, usually from right to left or left to right depending on how the relationship chain is described. In $P \text{ -- } Q \div R$, we first find the relationship between Q and R ($Q \div R$), then the relationship between P and Q ($P \text{ -- } Q$).
• Chain the Relationships: Combine the individual relationships to form the final relationship between the first and last person in the expression. For $P \text{ -- } Q \div R$: Q is R's father, and P is Q's brother. Therefore, P is the brother of R's father.
• Define Target Relationship: Clearly understand the target relationship you are looking for (e.g., paternal uncle, maternal aunt, nephew, niece). Define this relationship in terms of basic relations (e.g., paternal uncle = brother of father).
• Draw a Family Tree (Optional): For more complex problems, drawing a simple diagram or family tree based on the expression parts can help visualize the relationships and avoid confusion.
• Check Genders: Pay attention to the gender implied by the relationship symbols. For example, "brother" implies male, "sister" implies female, "father" implies male. This can help eliminate incorrect options.

Practicing various types of blood relation questions will improve your ability to quickly decode these symbolic expressions and solve reasoning puzzles.