August 1999
MA214 : DISCRETE MATHEMATICS

QUESTION 1 (Compulsory)

Total Marks: 20 Marks

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SUGGESTED SOLUTIONS
for Question 1

(a) (i) Give an example of an element of Z+.

(ii) Give an example of an element of Q.

(iii) Give an example of an element of Q Ç Z -.

(iv) Is the following relationship true or false?

R - Í Q

You must justify your answer.

 

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(b) Given matrics A = pic1.gif (1315 bytes)  and B = pic2.gif (1350 bytes),

Calculate

(i) AB

(ii) ABT

 

 

 

 

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(c) Write negations for each of the following statements:

(i) Lee is six feet tall and he weighs at least 90kg.

(ii) The bus was late or Edwin's watch was slow.

 

 

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(d) A student council consists of 15 students. In how many ways can a committee of six be selected from the committee?

 

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(e) Let A = {2,3,4} and B= {6,8,10} and define a binary relation R from A to B as follows:

" (x,y) Î A * B(x,y) Î R Û x | y

 

(i) Is 4 R 6? Justify your answer.

(ii) Is (2,10)Î R? Justify your answer.

 

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