3. Design Turing machines to decide the following languages. (10 Marks each)
(a) L = {a^{2i-1}c^{j}b^{2i-1} : i,j ? 1}
(b) L = {a^{2i+1}c^{j}b^{2i+1} : i,j ? 1}
(c) L = {a^i b^j c^{i+j} : i,j ? 1}
(d) L = {a^i b^j c^{i-j} : i,j ? 1}
(e) L = {xx : x ? {a,b}* }
(f) L = {xx^r : x ? {0,1}* }