April 2000
MA214 : DISCRETE MATHEMATICS

QUESTION 1 (Compulsory)

Total Marks: 30 Marks

• Question 2
• Question 3
• Question 4
• Question 5
• Cover Page

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SUGGESTED SOLUTIONS
for Question 1

(a)Draw a Venn diagram for sets A B and C that satisfy the following conditions:

(b)Which of the following conditional statements are true and which are false?Justify your answers.
(i)If 1 +1 =2,then 2 +2 =5.[1 mark ]
(ii)If 1 +1 =3,then 2 +2 =4.[1 mark ]
(iii)If 1 +1 =3,then 2 +2 =5.[1 mark ]
(iv)If 1 +1 =2,then pigs can fly.[1 mark ]
(v)If 2 +2 =4,then 1 +2 =3.[1 mark ]

(c)Let A be a 3 x 4 matrix,B be a 4 x 5 matrix,and C be a 4 x 4 matrix. Determine which of the following products are defined and find the size of those that are defined.
(i)AB
(ii)BA
(iii)CA
(iv)AA
[5 marks ]

(d)Use mathematical induction to prove that

whenever n is a nonnegative integer.[5 marks ]

(e)Consider the three graphs A,B and C shown below.

(i)Which graph is disconnected?[1mark ]
(ii)Which graph is a directed multigraph?[1 ark ]
(iii)Which graph is a pseudograph that is connected and not directed?[1 ark ]
Justify your answers.

(f)There are 325 computer science students at a school.How many ways are there to pick 3 representatives from these students?[2marks ]

(g)Evaluate

(h)Two fair dice are rolled.Calculate the probablity of:
(i)both dice showing 6;[1 mark ]
(ii)neither dice showing 6;[1 mark ]
(iii)at least one of the dice showing 6.[2 marks ]