Construct a dfa for the two simpler languages

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1. Prove that for all n∈N, n + n² is an even number.

2. Prove that for any full binary tree T, L(T) = 1 + I(T) where L(T) is the number of Leaf Nodes in T and I(T) is the number of internal nodes in T. For this question write the definition for L(T) and I(T) recursively.

3. The following language is the intersection of two simpler languages. Construct a DFA for the two simpler languages, then combine them using the construction discussed in footnote 3 (page 46) to give the state diagram of a DFA for the language given.

The alphabet is {a, b}. Assume the language is {w| w has at least 3 a's and at least 2 b's}.

Reference no: EM13679868

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