April 1999
MA214: DISCRETE MATHEMATICS

QUESTION 4

Total Marks: 20 Marks

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SAMPLE STUDENT'S SOLUTIONS
for Question 4

 
(a) Consider the statement S:

S = "if p is a prime number then p is odd"

 
(i) Write down the inverse of S. [1]
(ii) Write down the converse of S. [1]
(iii) Find counter examples to provide that none of these three statements are tautologies.

 

 [2]
(b) The fourth term in a geometric sequence is -72, and the seventh term in the sequence is +9.
(i) Calculate the common ratio. [2]
(ii) Write down the first three terms of the sequence. [1]
(iii) Calculate the sum to infinity of the sequence.

 

 [1]
(c) Construct the truth table for (~p « ~q) « (q « r)

 

 [4]
(d) What can you say about the sets A and B if the following are true?
(i) A È B = A [1]
(ii) A Ç B = A [1]
(iii) A - B = A [1]
(iv) A - B = B - A

 

 [1]
(e) Use algebraic laws show that pÙ(~pÚq) º pÙq [4]