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FORMAL LANGUAGE & AUTOMATA THEORYShow that the language: L = \{ a^{n^2} b^n \mid n \ge 0 \} is not regular.20227mFormal Language & Automata TheoryProve that the language L = \{a^{i^2} \mid i \ge 1\} is not context-free language.20197mDiscrete Mathematics(a) Prove the following: (i) There is a real number x such that x > 1 and 2^x > x^{10}. (ii) There is an integer n such that 2n^2 - 5n + 2 is prime.202210mDiscrete MathematicsWhich of the following two sets are equal? (i) A = \{1, 2\} and B = \{1\} (ii) A = \{1, 2\} and B = \{1, 2, 3\} (iii) A = \{1, 2, 3\} and B = \{2, 1, 3\} (iv) A = \{1, 2, 4\} and B = \{1, 2, 3\}20222m
Previous(a) Prove the following: (i) There is a real number x such that x > 1 and 2^x > x^{10}. (ii) There is an integer n such that 2n^2 - 5n + 2 is prime.Next(a) Show that p \lor (q \land r) and (p \lor q) \land (p \lor r) are logically equivalent. This is the distributive law of disjunction over conjunction.