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Key Concepts in Computer Science
[Proofs] 1. [10 marks] a) Prove using the rules of inference that the premises p --> q, -p --> r, r --> s imply ...
Continue reading[Basic Mathematics] 1. [5 marks] Find the tightest integer upper bound and lower bound for x if 𝒙= 𝐋𝐨𝐠𝟐(𝟓𝟐). Justify your answer. 𝟑𝟐<𝟓𝟐< 𝟔𝟒 ...
Continue reading1) [8 marks] Prove using mathematical induction that 3 + (3×5) + (3×52) + … + (3×5n) = (3×(5n+1 - 1))/4 whenever n is a nonnegative integer. Let P(n) be the following proposition:
Continue reading1) [6 marks] Show that each of these pairs of functions are of the same order. We should show that each of these functions are big-Theta of each other. One way is to show that each of them is big-O of ...
Continue reading1) [8 marks] Describe an algorithm that uses only assignment statements that replaces the triple (x; y; z) with (y; z; x). t := z x := y y := z z := t (where t is a temporary variable) 2) [10 marks] List all the ...
Continue reading1) [8 marks] Determine whether each of these functions from Z to Z is one-to-one. a) f(n) = n – 1 This is one to one. Any y ∈ codomain will get exactly one element from the domain (n + 1). b) f(n) ...
Continue reading1) [4 marks] Suppose that A = {2, 4, 7}, B = {2, 7}, C = {4, 7}, and D = {4, 6, 9}. Determine which of these sets are subsets of which other of these sets. B ⊆ A ...
Continue reading1) [4 marks] Use rules of inference to show that the hypotheses a) Randy works hard b) If Randy works hard then he is a dull boy c) If Randy is a dull boy, then he will not get the job implies the conclusion ...
Continue reading1. [2 marks] Show that (¬q (p q)) ¬p is a tautology using truth table. We showed that all of the rows are True. Therefore, the statement is a tautology. 3. [3 marks] Give a ...
Continue reading1. [6 marks] Plot the three functions y=x2, y=2x2, y=x2+2 on the same X-Y graph for {x | -3 ≤ x ≤ 3}. 2. [6 marks] Write pseudocode ...
Continue reading1. [1 mark] What is Log4(1024)? Show how you determine the result. 𝟏𝟎𝟐𝟒= 𝟒𝟓 Log4(1024) = 𝐋𝐨𝐠𝟒(𝟒𝟓)=𝟓· 𝐋𝐨𝐠𝟒(𝟒) = 5 2. [2 marks] Given 𝐋𝐨𝐠𝟔(𝒙)=𝟐 solve for x. Show how you determine the result. 𝐋𝐨𝐠𝟔(𝒙)=𝟐 ⟹ 𝟔𝟐=𝒙 ⟹𝒙=𝟑𝟔 This is derived from the definition ...
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