Solution

The correct answer is {z, x}

Explanation:

To find the Follow set of the non-terminal R in the given grammar, we will analyze the production rules.

Grammar:
1. T → Qx
2. Q → RS
3. R → y | ϵ
4. S → z | ϵ

Step 1: Identify the rules involving R

From the production Q → RS :

• R appears before S , and we need to determine what can follow R .

Step 2: Determine Follow set of R

1. Check the Follow of Q :

• From T → Qx , the Follow of Q includes x .
• Thus, Follow(Q) = {x} .

2. From Q → RS :

• The symbols that can follow R are the symbols in the Follow set of S .

Step 3: Determine Follow of S

1. Check the productions for S :

• From S → z | ϵ :
• If S produces ϵ , we also consider what follows S in Q .

2. Follow of S :

• From Q → RS :
  • The symbols that can follow S include the Follow of Q , which is x (from T ).
• Thus, Follow(S) = {x} .

Step 4: Combine results for R

Since S can produce ϵ :

• The Follow set of R will include everything in Follow(S) plus anything that follows Q .
• Therefore, the Follow set of R includes:
  • The Follow of S : x
  • The Follow of Q : Since R is at the end of Q , we include whatever follows Q .

Final Step: Conclusion

Combining all the above information, the Follow set of R is: Follow(R) = {z, x}

However, since R produces y (and indirectly through Q ), and because R is followed by S which can produce ϵ , we include z in Follow of R .

Thus, the correct answer is: 3) {z, x}