Which representation of grammar corresponds to the a(aUb)*b expression?a)(1) S →→ bMa (2) M →→ eb (3) M →→ abM (4) M →→ baMb)(1) S →→ aMb(2) M →→ e(3) M →→ aMb(4) M →→ bMac)(1) S →→ aMb (2) M →→ e (3) M →→ aM (4) M →→ bMd)(1) S →→ baMab (2) M →→ ea (3) M →→ abM (4) M →→ baMe)(1) S →→ aMb(2) M →→ Mab(3) M →→ aM(4) M →→ bM
Question
Which representation of grammar corresponds to the a(aUb)*b expression?a)(1) S →→ bMa (2) M →→ eb (3) M →→ abM (4) M →→ baMb)(1) S →→ aMb(2) M →→ e(3) M →→ aMb(4) M →→ bMac)(1) S →→ aMb (2) M →→ e (3) M →→ aM (4) M →→ bMd)(1) S →→ baMab (2) M →→ ea (3) M →→ abM (4) M →→ baMe)(1) S →→ aMb(2) M →→ Mab(3) M →→ aM(4) M →→ bM
Solution
The correct representation of the grammar that corresponds to the expression a(aUb)*b is:
b) (1) S →→ aMb (2) M →→ e (3) M →→ aMb (4) M →→ bMa
This is because the expression a(aUb)*b can be broken down as follows:
- The first 'a' corresponds to the first 'a' in the grammar rule (1) S →→ aMb.
- The (aUb)* part corresponds to the grammar rules (3) M →→ aMb and (4) M →→ bMa, which allow for any combination of 'a's and 'b's.
- The final 'b' corresponds to the 'b' in the grammar rule (1) S →→ aMb.
- The 'e' in rule (2) M →→ e allows for the possibility of no 'a's or 'b's in the middle of the expression, as indicated by the * in the expression a(aUb)*b.
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