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Use the pumping lemma to show that the following languages are not context free: a) {0^n #0^2n#0^3n | n ? 0} b) {w#x where

Use the pumping lemma to show that the following languages are not context free:

a) {0^n #0^2n#0^3n | n ? 0}

b) {w#x \ where w,x ? {a,b}* and w is a substring of x}

c) {a^i b^j a^i b^j | i,j?0}

d) {xcx | x?{a,b}*}

e) {x1#x2# ... #xk | k ? 2, xi ? {a,b}*, and for some i ? j, xi = xj}

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