Step-by-Step Analysis

To find the correct expression for "R is brother of T", we first need to understand the meaning of each symbol and then analyze each option to see which one builds the required relationship.

1. Symbol Definitions

• P ψ Q means P is the mother of Q.
• P ∈ Q means P is the sister of Q.
• P \ Q means P is the father of Q.
• P # Q means P is the brother of Q.

2. Target Relationship

The statement "R is brother of T" requires two conditions to be met:

1. R must be male.
2. R and T must be siblings (i.e., they share the same parent/s).

3. Evaluating the Options

A. R ψ S # U \ T

• The first part, R ψ S, means "R is the mother of S". This establishes R as female.
• Therefore, this option cannot mean "R is brother of T".

B. U ψ R # S # T

• U ψ R means "U is the mother of R".
• R # S means "R is the brother of S". This establishes that R is male and that R and S are siblings (with mother U).
• S # T means "S is the brother of T". This establishes that S and T are siblings.
• Since R is a sibling of S, and S is a sibling of T, it follows that R is also a sibling of T. As we already know R is male, this expression correctly means "R is the brother of T".

C. U ψ R ∈ S ψ T

• The second part, R ∈ S, means "R is the sister of S". This establishes R as female.
• Therefore, this option cannot mean "R is brother of T".

D. T # S \ Q = R

• This option is ambiguously written. Assuming it means T # S, S \ Q, and Q ∈ R, it would make T the brother of S, who is the father of R. This would make T the uncle of R, not the brother.

Conclusion

The only expression that logically establishes R as the brother of T is U ψ R # S # T.