Prove that the sum of an even integer and an odd integer is odd. Let n₁ be an even integer, and let n₂ be an odd integer. So n₁ = n₁ + n₂ = + 1 = for some integer k₂ and n₂ = (K₁ + K₂) + 1 is -Select-- for some integer k₂. Then
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- Show that for f(n) = 2n2 and g(n) = 20n + 3n2 , f(n) is θ(g(n)). How many ways can it be shown? Also Show that for g(n) = 10n2and f(n) = n! + 3 , f(n) is Ω(g(n)). How many ways can it be shown? Discuss with the instructor.If a is a symbol and n > 0, then an denotes a···a, or in words, the string of length n consisting of only a’s. Now consider the coding with two code words 0n and 1n, for some natural number n > 0. Show that this coding is perfect if and only if n is odd.Prove by Induction that for all integers n ≥ 1, n < n2 + 1 .Yes this problem is silly, but still do it by induction! Prove by Induction that for all integers n ≥ 3, 2n < n2 .