Give context-free grammars that generate the following languages. In all parts the alphabet is {0, 1}.

a) {w | w contains at least three 0s}

b) {w | the length of w is even}

c) {w | w starts and ends with the same symbol}

d) {w | the length of w is odd and its middle symbol is a 1}

e) {w | w = w R , that is, w is a palindrome}

f) The empty set

aand Give pushdown automata for the languages in question