How to construct DFA and NFA?

1. Construct a DFA recognizing the following language {w| w contains an even number of 0s, or contains exactly two 1s}

2.

Construct an NFA recognizing the following language a. {w| w contains an even number of 0s, or contains exactly two 1s}

b. {w| w starts with 0 and has an odd length or starts with 0 and has even length}

Use the pumping lemma to show that the following languages are not regular.

1. . A1 = {0n1n2n| n 0}

2. A2 = {www| w {a, b}}

3. A3 = {a2n | n 0} (Here, a^2^n means a string of 2^n as.)