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Sma2113:Maths For Science Question Paper
Sma2113:Maths For Science
Course:Bachelor Of Computer Science
Institution: Meru University Of Science And Technology question papers
Exam Year:2012
QUESTION ONE – (30 MARKS)
(a) Consider the function of : defined by = 2 . Determine (i) 1:4 25 (2 Marks)
(ii) 19 (2 Marks)
(b) Let = 1,1, 2,3, 3,2 be the relation on = 1,2,3. Determine whether is (i) Reflexive (2 Marks) (ii) Symmetric (2 Marks) (iii)Transitive (2 Marks) (c) Show that the set of all integers under the binary operation defined by = + + 3, , is an abelian group. (5 Marks)
(d) Consider the binary operation table below defined over a set = ,,,
a b c d a a b c d b b a c d c c d c d d d c c d
2
Determine whether in the table satisfies (i) Commutative law (3 Marks) (ii) Associative law (3 Marks)
(e) Let and be two permutations defined on = ,,, as, follows: ? ? ? ?
? ? ? ?
?
bdac dcba f and ? ? ? ? ? ? ? ? ? adcb dcba g Show that the composition of these two permutations is not commutative. (4 Marks)
(f) Let = 1,2,3,4,5 : be defined by the diagram.
Find: (i) 1,3,5 (1 Mark)
(ii) 12,3,4 (2 Marks)
(iii) 13,5 (2 Marks)
QUESTION TWO – (20 MARKS)
(a) Let = 1,2,3,4 , ,,, = 5,6,7,8 and let = 1,, 1,, 2,, 3,, 4, and = ,5, ,6, ,8, ,7 Determine (7 Marks)
(b) Let be the relation < from = 1,2,3,4 = 1,3,5.
(i) Write as a set of ordered pairs. (2 Marks) (ii) Plot on a coordinate diagram of × . (4 Marks) (iii) Find the domain of , range of and 1. (3 Marks) (iv) Find 1 (4 Marks)
1 2 3 4 5
1 2 3 4 5
3
QUESTION THREE – (20 MARKS)
(a) Prove that the set of non-zero integers modulo 6 under 6 is not a group. (6 Marks)
(b) Show that the set G composed of 1,2, 3, 4 of 4 transformations of the set of complex numbers in itself defined by 1 = , 2 = , 2 = 1 , 4 = 1 , is an Abelian group with composite operation ., where = 1,2,3, 4 : . (14 Marks)
QUESTION FOUR – (20 MARKS)
(a) Given that are two permutations of 7, where ? ? ? ?
? ? ? ?
?? ? ? ?
? ? ? ?
?
3124567 7654321
1234567 7654321 ?? and Find
(i) 1 (3 Marks)
(ii) 1 1 (4 Marks)
(b) Find the group of symmetries of a regular hexagon. (6 Marks)
(c) Prove that = 0,2,4,+6 is a subgroup of the group of integers modulo 6. (7 Marks)
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