Understanding Blood Relations through Symbol Codes

This question asks us to interpret symbolic relationships to determine which given expression correctly represents the statement: "Z is brother of W's wife", given that Z is male.

Decoding the Symbols

First, let's break down the meaning of each symbol provided:

• P $ Q: P is the husband of Q. This means Q is the wife of P. This establishes a married couple relationship.
• P ! Q: P is the mother of Q. This means Q is the child of P. This establishes a parent-child relationship.
• P * Q: P is the daughter of Q. This means Q is the parent of P. This establishes a parent-child relationship, specifying the child's gender.

Analyzing the Target Relationship

The goal is to find an expression where Z is brother of W's wife. Let's identify the required connections:

• We need to find W's wife. Let's call her 'A'. So, W is the husband of A (W $ A).
• We need Z to be the brother of A. This means Z and A are siblings, and Z is male.

So, we are looking for a relationship chain that starts with W, leads to his wife, and then shows Z as that wife's brother.

Evaluating Each Option

Let's examine each option step-by-step based on the defined relationships:

Option 1: W * X ! Y $ Z

• W * X: W is the daughter of X. (X is parent of W)
• X ! Y: X is the mother of Y. (Y is child of X)
• Y $ Z: Y is the husband of Z. (Z is wife of Y)

From W * X and X ! Y, W and Y are siblings (both children of X). From Y $ Z, Z is the wife of Y (W's brother). This does not show Z as the brother of W's wife.

Option 2: W $ X ! Y * Z

• W $ X: W is the husband of X. (X is wife of W)
• X ! Y: X is the mother of Y. (Y is child of X)
• Y * Z: Y is the daughter of Z. (Z is parent of Y)

From W $ X, X is W's wife. From X ! Y, X is mother of Y. From Y * Z, Y is daughter of Z. Since X is mother of Y and Z is parent of Y, Z must be the father of Y, and X's husband/partner. This means Z is W's wife's husband/partner (and father of her child Y). This is not the required relationship.

Option 3: W * X $ Y ! Z

• W * X: W is the daughter of X. (X is parent of W)
• X $ Y: X is the husband of Y. (Y is wife of X)
• Y ! Z: Y is the mother of Z. (Z is child of Y)

From X $ Y, Y is wife of X. From Y ! Z, Y is mother of Z, so X is father of Z. From W * X, W is daughter of X. Since X is parent of W and parent of Z, W and Z are siblings. This option shows W and Z are siblings, and X is their parent (father). This does not establish Z as brother of W's wife.

Option 4: W $ X * Y ! Z

• W $ X: W is the husband of X. (X is wife of W)
• X * Y: X is the daughter of Y. (Y is parent of X)
• Y ! Z: Y is the mother of Z. (Z is child of Y)

From W $ X, we know X is W's wife. This matches the first part of our target relationship. Now let's look at the rest: From X * Y, X is the daughter of Y. This means Y is the parent of X. From Y ! Z, Y is the mother of Z. This means Y is the parent of Z. Since Y is the parent of both X and Z, X and Z are siblings.

We established that X is W's wife and that X and Z are siblings. The question states that Z is male. Therefore, Z is the male sibling of X, who is W's wife. This means Z is the brother of W's wife.

This option correctly represents the required relationship.

Conclusion

Based on the step-by-step evaluation of each option, the expression W $ X * Y ! Z is the only one that shows Z as the brother of W's wife, given that Z is male.

Blood Relations Reasoning Revision Table

Additional Information on Blood Relations Puzzles

Blood relations questions using symbols test your ability to decode relationships and build a family tree or chain of connections. It's crucial to decode each link in the chain sequentially from left to right (or as indicated by the expression). Always pay attention to the gender of individuals if specified, as it is often critical for solving the puzzle, as seen with the condition that Z is male in this question. Practice with different symbols and relationships helps improve speed and accuracy.