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Discrete 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.202210mFormal Language & Automata TheoryConstruct a DFA which accepts the set of all binary strings that interpreted as binary representation of an unsigned decimal integer, is divisible by 5.20207mArtificial intelligenceWrite a function in LISP that computes prime number between 1 and 25 (inclusive).20227mDiscrete MathematicsLet A be the set odd positive integers less than 10. Then cardinality of A, ∣A∣ is (i) 5 (ii) 9 (iii) 6 (iv) 420232m
PreviousState and prove Division algorithm theorem well-ordering principle.NextA grocery store employee is stocking apples. Each apple is a different color. There are 10 apples left in the box and the employee pulls out 2 of them at random. What is the probability that the employee pulls out one pink apple and yellow apple?