Grammar Reduction

Step 1: Reducing the grammar.
The given grammar contains several rules that can be reduced. We will look at the productions involving non-terminal and attempt to eliminate unnecessary rules.

1. : This production can be kept as is.

2. : Substitute from the first rule, so , which can be reduced.

3. : Can be reduced by eliminating in subsequent steps.

4. : Reduced to a single rule.

5. : A single rule for .

6. : This can be reduced to a simpler production.

After simplifying the above rules, we are left with 5 production rules in total.

Step 2: Conclusion.
Thus, the correct number of reduced productions is 5, so the correct answer is (3) Five.