TRUE or FALSE L1 (a b* a) L2 (ab* + aa* b) L3 = L1 L2 L4 = L1 + L2 Question 1: U

Question

TRUE or FALSE

L1 (a b* a) L2 (ab* + aa* b)

L3 = L1 L2 L4 = L1 + L2

Question 1: Using the above language definitions, determine whether the given string is an element of the given language:

Question 2: Using the above language definitions, determine whether the given string is an element of the given language:

Question 3: Using the above language definitions, determine whether the given string is an element of the given language:

Question 4: Using the above language definitions, determine whether the given string is an element of the given language:

Explanation / Answer

1, aabb does not belong to L3 because L3=L1L2 and L1 in the minimal string requires 2 a's and L2 in the minimal string also require 1 a. So to a string which belongs to L3 must have atleast 3 a's.

2. abab also does not belong to L3 for the same reason mentioned in answer 1.

3. abaa does not belong to L4 because L4= L1 + L2 ,i.e., L1 or L2 and abaa cannot be generated by either L1 or L2.

4. aaab belongs to L4 because it can be generated by L2. aa*b can generate aaab.

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