April 2000
MA214 : DISCRETE MATHEMATICS

QUESTION 2

Total Marks: 15 Marks

• Question 1
• Question 3
• Question 4
• Question 5
• Cover Page

SUGGESTED SOLUTIONS
Solutions and allocated marks are indicated in green.
Return to Question 2

(a)Let A ={a, b, c },B ={b, c, d }and C ={b, c, e }.
Write down the elements that are contained in the following sets.

Are any of these sets equal?[7marks ]

Two marks. Subtract one mark for every error or omission up to a maximum of two. [7 marks ]

(b)Recall that P(A) denotes the set of all subsets of A
(i)Write down P( {a, b, c })[3marks ]
(ii)A function F :P( {a, b, c }) {0 , 1 , 2 , 3 }is defined by
F(X ) =the number of elements in X
Write down F(X ) for each X P( {a, b, c })[5marks ]
(i)P( {a, b, c }) ={, {a }, {b }, {c }, {a, b }, {a, c }, {b, c }, {a, b, c }}Three marks.
Subtract one mark for every error or omission up to a maximum of three. [3 marks ]
(ii)
F( ) =0
F( {a }) =1
F( {b }) =1
F( {c }) =1
F( {a, b }) =2
F( {a, c }) =2
F( {b, c }) =2
F( {a, b, c }) =3
Five marks. Subtract one mark for every error or omission up to a maximum of five. [5 marks ]