Consider the grammar defined by the following production rules, with two operators $*$ and $+$ $$S \rightarrow T * P$$ $$T \rightarrow U \mid T * U$$ $$P \rightarrow Q + P \mid Q$$ $$Q \rightarrow Id$$ $$U \rightarrow Id$$ Which one of the following is TRUE?

To determine the associativity of operators from context-free grammar productions:

1. **For operator $*:** The production rule is$T \rightarrow T * U \mid U$. Since the non-terminal$T$appears on the leftmost position on the right-hand side ($T \rightarrow T * U$), the production is left-recursive. Therefore, the operator $*$ is left-associative.

2. For operator $+: The production rule is $P \rightarrow Q + P \mid Q$. Since the non-terminal $P$ appears on the rightmost position on the right-hand side ($P \rightarrow Q + P$), the production is right-recursive. Therefore, the operator $+$ is right-associative.

Hence, $+$ is right associative, while $*$ is left associative, which corresponds to option (B).