# MATH221-2019S1-Class Test.pdf - Math221 – Mathematics for...

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MATH121 Session 1, Jan-Mar 2019Page 1 of 2Math221 – Mathematics for Computer ScienceClass TestSession 1, January – March 2019Duration: 1 hour 30 minutesThis paper has SIX questions. Answer ALL the questions.Question 1LetP,QandRbestatements. Prove the following:((PQ)R)(P(QR))(10 marks)Question 2(a)LetP,QandRbe simple statements. Construct the truth table for thecompound statement.()()[]RPQPR~Hence, determine whether it is a tautology, contradiction or contingentstatement.(12 marks)(b)Write the following statements using quantifiers:(i)The square of any integer is odd.(4 marks)(ii)Everybody is older than somebody.(4 marks)Question 3Find the simplest expression for the following set. Justify each of the steps by citingthe set theory rule used.��𝐴𝐴̿∩ 𝐵𝐵� ∪ 𝐴𝐴̅� ∪ �(𝐵𝐵∩ 𝐴𝐴)(𝐵𝐵∩ 𝐵𝐵)(20 marks)Question 4(a)Using a suitable form of Mathematical Induction, prove the following.1 + 4 + 7 + … + (3n– 2) =𝑛𝑛(3𝑛𝑛−1)2
MATH121 Session 1, Jan-Mar 2019Page 2 of 2
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