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TCC122 Discrete Structures 2

Question

Answered

1(a) Jeniffer has 5 different types of little pony soft toys. The soft-toys characters are Twilight Sparkle (purple colour), Apple Jack (orange colour), Pinkie Pie (pink colour), Fulttershy (yellow colour) and Rainbow Dash (cyan colour). She chooses TWO (2) colours (from the soft toys) from the collection.
(i)
How many colour combinations are possible?
 
(ii)
List ALL of the combinations.
 
(b) Michael has 4 printed articles download from different online publishers. They are IEEE xplore, Elsevier, Proquest and Emerald Insight.
(i)
How many different arrangements are possible if he wishes to rearrange the Printed articles?
 
(ii)
Assume Proquest is one of the sub unit from Emerald Insight, how many different arrangements are possible?
 
 
2 Let R = {(1, 2), (1, 3), (1, 4), (2, 1), (2, 3), (2, 4), (3, 1), (3, 2),(3, 4), (4, 1), (4, 2), (4, 3)}
(a)
Represent each of the relation in a matrix form.
 
(b)
Draw the digraph.
 
(c)
Determine R’s characteristics (i.e: reflexive, symmetric, transitive).
 
(d)
Is R equivalent? Justify.
 
 
23. Suppose that James deposited RM 5,000 in a saving account of a bank with an interest rate of 4% per year compounded annually.
(a)
If the interest is calculated based on the ‘principle’ only, what is the total amount after 6 years? Draw a table to include the principle and the amount earned at the end of each year.
 
(b)
If the interest is calculated based on the ‘total principle and interest’, what is the total amount after 6 years? Draw a table to include the new principles and the amount earned at the end of each year.
 
(c)
Based on the amount obtained from 3(a) and 3(b), which method (i.e. (a) or (b)) will you choose? Why?

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