In a certain code language,
'A B' means 'A is the mother of B', 'A # B' means 'A is the father of B', 'A ! B' means 'A is the sister of B', 'A @ B' means 'A is the brother of B', 'A * B' means 'A is the wife of B', 'A > B' means 'A is the husband of B', 'A % B' means 'A is the father-in-law of B', 'A ^ B' means 'A is the mother-in-law of B'. Based on the above, how is U related to A if: a) 'P > Q R > S ! T',
b) 'U # T',
c) 'R # A'?

Let us decode the relational expressions step by step to determine the link between U and A:
From expression (a): P > Q $R>S!TP>Q\to PisthehusbandofQ(Qisfemale).Q$ R→ Q is the mother of R.

R>S→ R is the husband of S (S is female). So R is a son of P and Q.

S!T→ S is the sister of T.

From expression (b): U # T

U is the father of T. Since S and T are siblings, U is also the father of S.

From expression (c): R # A

R is the father of A.

Now, let's establish the connection between U and A:

A's father is R.

R's wife is S. So, S is the mother of A.

S's father is U.

Therefore, U is the father of A's mother, which means U is A's Mother's father (maternal grandfather).