5. (6 marks) Let E = {a,b,c,d}. Give context-free grammars that generate the following languages. In each case, also give a derivation of the specified terminal string using your grammar. The derivation beginning from the start variable should indicate each individual derivation step using the notation (a) L1 = {b2i c3k+1 | k > i>0} Derivation for the string: b2c4. (b) L2 = {azib2i+1c5k+2 | i > 1, k > 1} Derivation for the string: a4b5c?. (c) L3 {a2163i+1,38+1 di +1 | i > 1,7 > 1,8 > 1} Derivation for the string: a4b4c7d2 (d) L4 = {a3i+1fi+3c2kdJ2k | i > 0, k > 0} U {a_rb c58 4"+1 r > 0,8 >0} Derivation for the string: a%bc%d