Using the pumping lemma, prove that the language

a). L1 = {w {a}* | w = a ^(kk) with k 0}

The language L1 thus contains only words that consist of a quadratic number of a, for example a, aaaa, etc.

b). L2 = {w {0, 1}* | |w0| |w1|}

So the L2 language contains only words that have different numbers of zeros and ones.

c). L3 = {w {0, 1}* | w is palindrome }

d). L4 = {0^(p1+p2) | p1 and p2 are primes }

e). L5 = {0^(i) 1^(2i) | i 0}

f). L6 = {0^(i) 0^(2i) | i 0}