December 1999
MA214 : DISCRETE MATHEMATICS

QUESTION 5

Total Marks: 15 Marks

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SUGGESTED SOLUTIONS
for Question 5

(a)

How many bit strings of length eight either start with a 1 bit or end with the two bits 00?

 

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(b)

Assume that in a group of six people, any pair of individuals consists of either two friends or two enemies. Show that there are either three mutual friends or three mutual enemies in the group.

 

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(c)

A study was carried out to determine the efficiency of three different drugs A,B and C in relieving headache pain.The following results were obtained

40 subjects were given the chance to use all three drugs
23 reported relief from drug A
18 reported relief from drug B
31 reported relief from drug C
11 reported relief from both drugs A and B
19 reported relief from both drugs A and C
14 reported relief from both drugs B and C
 37 reported relief from at least one of the drugs


Note that some of the 23 subjects who reported relief from drug A may have also reported relief from drugs B or C, with similar remarks applying to other data.


(i)How many people got relief from none of the drugs?[1 mark ]


(ii)How many people got relief from all three drugs?[2 marks ]


(iii)Let A be the set of all subjects who got relief from drug A,B the set of all subjects who got relief from drug B,and C the set of all subjects who got relief from drug C.Make a copy of the diagram shown below and fill in the numbers for all eight regions.[2 marks ]

(iv)How many subjects got relief from A only?[1 mark ]

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