Table Of Content
Table of Contents
Learning Outcome 01 .............................................................................................................. 5
Part – 1............................................................................................................................... 5
1. Let U = {l, 2, 3, 4, 5, 6, 7, 8, 9, and 10} be a universal set. Let A, B, C such that A= {l, 3, 4,
8}, B = {2, 3, 4, 5, 9, 10}, and C = {3, 5, 7, 9, 10}. Use bit representations for A, B, and C
together with UNION, INTER, DIFF, and COMP to find the bit representation for the
following: ............................................................................................................................ 5
Part - 2 ............................................................................................................................... 6
2.1 Write the multisets of prime factors of given numbers. .................................................... 6
2.2 Write the multiplicities of each element of multisets in part 2(1-I, ii, iii) separately. ......... 6
2.3 Find the cardinalities of each multiset in part 2-1. ............................................................ 7
Part – 3............................................................................................................................... 8
3. A student has 37 days to prepare for an exam. From past experience, he knows that he will
need no more than 60 hours of study. To keep from forgetting the material, he wants to study
for at least one hour each day. Show that there is a sequence of successive days during which
he will have studied exactly 13 hours.................................................................................... 8
3.1 A certain computer system breaks down in two mains. Ways: faults on the network and
power supply faults. Of the last 50 breakdowns,42 involved network faults and 20 power
failures. In 13 cases, both the power supply and the network were faulty. How many
breakdowns were attributable to other kinds of failure? ......................................................... 9
Part - 4 ............................................................................................................................. 10
4. ...................................................................................................................................... 10
i. Write a function that represents the total monthly cost C(x) of Mary Ann’s cell ................ 10
ii. Find the inverse function ................................................................................................ 10
iii. What do x and C-1(x) represent in the context of the inverse function? ........................... 10
iv. How many additional minutes did Mary Ann use if her bill for her third month was $48.89?
......................................................................................................................................... 10
4.1. An online music subscription service allows members to download songs for $0.99 each
after Paying a monthly service charge of $3.99. The total monthly cost C(x) of the service in
dollars is C(x)=3.99 +0.99x, where x is the number of songs downloaded. ........................... 11
i. Find the inverse function ................................................................................................. 11
ii. What do x and C-1(x) represent in the context of the inverse function? ............................ 11
iii. How many songs were downloaded if a member’s monthly bill is $27.75? ..................... 11
Learning Outcome 02 ............................................................................................................ 12