2. Using the pumping lemma and contradiction, prove that L= (abn>m}! is not regular.
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Use the pumping lemma and contradictions to prove the language is not regular.
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- ¬P ∧¬Q≡¬(P ∨Q) Prove the following equivalency relation (Proof, Justification/explanation):For each of the following recurrence relations, write down the running timeT(n) if it can be solved with the Master Theorem. Otherwise, indicate why the MasterTheorem does not apply.4. Show that (p → q) ∧ (p → r) and p → (q ∧ r) are logically equivalent using equivalencelaw.
- prove the equivalence of the schemata:~(~(p • ~ q ) • ~ ( ~ p• q)) equal to ~(p • q) • ~(~p • ~q)Using the pumping lemma, show {a^n b^m a^m b^n} is nonregular language. Show it by listing all possible cases of substring y and considering each of them using the pumping lemma. How many possible cases of substring y exist?Solve the following recurrence relations using Master theorem. a. ?(?) = 3? (?/2) + ????? b. ?(?) = ? (9?/10) + ?