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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 ๐= ๐๐จ๐ ๐(๐๐). Justify your answer. ๐๐<๐๐< ๐๐ ...
Continue reading1) [8 marks] Prove using mathematical induction that 3 + (3ร5) + (3ร52) + โฆ + (3ร5n) = (3ร(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 โ 1 This is one to one. Any y โ 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. ๏ท B โ A ๏ท ...
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 (ยฌq ๏ (p ๏ฎ q)) ๏ฎ ยฌp 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 โค x โค 3}. 2. [6 marks] Write pseudocode ...
Continue reading1. [1 mark] What is Log4(1024)? Show how you determine the result. ๐๐๐๐= ๐๐ Log4(1024) = ๐๐จ๐ ๐(๐๐)=๐ยท ๐๐จ๐ ๐(๐) = 5 2. [2 marks] Given ๐๐จ๐ ๐(๐)=๐ solve for x. Show how you determine the result. ๐๐จ๐ ๐(๐)=๐ โน ๐๐=๐ โน๐=๐๐ This is derived from the definition ...
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