Suppose A → xBz and B → y, then the simplified grammar would be:Select one:a. None of the mentionedb. A → xBz|xyzc. A → xyz d. A → xBz|B|y

To solve this grammar simplification problem, we will analyze the production rules given and see how they can be simplified.

1. Break Down the Problem

• We have two production rules:
  • $A \rightarrow xBz$
  • $B \rightarrow y$
• We need to determine how to express $A$ using this information while considering the possibilities of simplification.

2. Relevant Concepts

• From the rule $B \rightarrow y$, we can replace $B$ in the production for $A$.
• The production for $A$ could potentially incorporate the production for $B$.

3. Analysis and Detail

1. Rewrite the production of $A$:
   • From $A \rightarrow xBz$, substituting $B \rightarrow y$ gives: $A \rightarrow xy z$
2. Looking at the structure, we have:
   • $A$ can produce $xBz$ which by substituting $B \rightarrow y$ gives a specific string.
   • The possibility of $B$ producing $y$ can also exist within $A$ if we want to keep both forms.
3. Thus, we consider the alternatives:
   • $A$ can produce $xBz$ or also produce the derived $y$.

4. Verify and Summarize

• The possible productions we can write from the evaluations are:
  1. $A \rightarrow xBz$
  2. $A \rightarrow xy z$ through substitution.

Given this, we analyze the provided options:

1. None of the mentioned - doesn't apply as we have valid productions.
2. A → xBz | xyz - is valid.
3. A → xyz - is incomplete.
4. A → xBz | B | y - doesn’t reflect simplification properly.

Thus, based on our analysis, the most appropriate simplified grammar that follows all necessary rules while catering to the substitutions is:

Final Answer

b. A → xBz | xy