CUSTOMER_CODE
SMUDE
DIVISION_CODE
SMUDE
EVENT_CODE
SMUAPR15
ASSESSMENT_CODE MCA1030_SMUAPR15
QUESTION_TYPE
DESCRIPTIVE_QUESTION
QUESTION_ID
10111
QUESTION_TEXT Explain the 2 methods of representing a set
SCHEME OF
EVALUATION
There are two methods of representing a set:
i.Roster or tabular form
ii.Set builder form
i.In roster form, all the elements of a set are listed, the elements being
separated by commas and are enclosed within braces { }. For
example, the set of all even positive integers less than 7 is described
in roster form as {2, 4, 6}.
It may be noted that while writing the set in roster form an element is
not generally repeated, i.e all the elements are taken as distinct.
ii.In set builder form, all the elements of a set possess a single
common property which is not possessed by any element outside the
set. For example, in the set “{a, e, i, o, u}” all the elements possess a
common property, each of them is a vowel in the English alphabet
and no other letter possesses this property. Denoting this set by V, we
write V= {x: x is a vowel in the English alphabet}
QUESTION_TYPE
DESCRIPTIVE_QUESTION
QUESTION_ID
10114
QUESTION_TEXT
Define the following with an example: Empty set, finite and
infinite set, equal sets, subsets, powerset
SCHEME OF
EVALUATION
Solution: Empty set: A set which does not contain any element is
called an empty set or null set
Ex: P={x:1<x<2, x is a natural number}
Finite and infinite set: A set which is empty or consists of a definite
number of elements is called finite. Otherwise the set is called
infinite.
Ex: A={1, 2, 3, ….}infinite
B={1, 2, 3}finite
Equal sets: 2 sets A and B are said to be equal if they have exactly
the same elements and we write A=B
Ex: Let A ={1, 2, 3, 4}, B={3, 4, 1, 2}
Then A=B
Subsets: If every element of a set A is also an element of a set b,
then A is called a subset of B denoted by A C B
Ex: A={1, 2, 3, 4}, B={0, 1, 2, 3, 4, 5}
Then A C B
Power set: The collection of all subsets of a set A is called the
power set of A, denoted by P(A)
Ex: A={1, 2}
Then P(A)= {∅, {1}, {2}, {1, 2}}
QUESTION_TYPE
DESCRIPTIVE_QUESTION
QUESTION_ID
74003
QUESTION_TEXT
Let p: The south-west monsoon is very good this year.
q: Rivers are rising
Give the verbal translation of
i. ~ [(~p) v (~q)]
ii. p  q
iii. (p v q) v (~p)
iv. ~ (p ^ q)
v. (~p) ^ (~q)
SCHEME OF
EVALUATION
i. The south-west monsoon is very good this year and rivers are
rising.
ii. If the south-west monsoon is very good this year then the
rivers are rising.
iii. The south-west monsoon is very good this year or the rivers
are rising or the south-west monsoon is not very good this year.
iv. The south-west monsoon is not very good this year or the
rivers are not rising.
v. The south west monsoon is not very good and the rivers are
not rising.
(2  5 = 10 marks)
QUESTION_TYPE
DESCRIPTIVE_QUESTION
QUESTION_ID
74004
Explain the cartesian product of Sets.
QUESTION_TEXT
SCHEME OF
EVALUATION
Solution:
Let A, B be two sets. If a is in A, b is in B, then (a, b) denotes an
ordered pair whose first component is a and the second component
is b. Two ordered pairs (a, b) and (c, d) are said to be equal if and
only if a = c and b = d. (2 marks)
In the ordered pair (a, b), the order in which the elements a and b
appears in the bracket is important. Thus (a, b) and (b, a) are two
distinct ordered pairs if a not equal to b. Also, an ordered pair (a, b)
is not the same as the set {a, b}. (2 marks)
Definition: The set of all ordered pairs (a, b) of elements a is in A, b
is in B is called the Cartesian Product of sets A and B and is denoted
by A x B. Thus
A x B={(a, b): a is in A, b is in B}.
Let A={a1, a2}, B={b1, b2, b3. To write the elements of A x B, take a1
is in A and write all elements of B with a1, i.e., (a1, b1), (a1, b2), (a1,
b3). Now take a2 belongs to A and write all the elements of B with
a2, i.e., (a2, b1), (a2, b2), (a2, b3). Therefore, A x B will have six
elements, namely (a1, b1), (a1, b2), (a1, b3), (a2, b1), (a2, b2), (a2,
b3) (6 marks)
QUESTION_TYP
DESCRIPTIVE_QUESTION
E
QUESTION_ID
124969
Let A={1, 2, 3}, B={3, 4} and C={4, 5, 6}. Then find
i.
A×(B∩C)
QUESTION_TEX ii. (A×B)∩(A×C)
T
iii. A×(B∪C)
iv. (A×B)∪(A×C)
SCHEME OF
EVALUATION
i.
We have
ii.
We note that
and
. Therefore,
Therefore
iii.
Clearly
iv.
In view of (ii), we see that
. Thus
QUESTION_TYPE
DESCRIPTIVE_QUESTION
QUESTION_ID
124975
QUESTION_TEXT
Explain the concept of complex numbers. Briefly explain two
properties of complex numbers for addition and multiplication.
Let C denote the set of all ordered pairs of real numbers.
SCHEME OF
EVALUATION
i.e., C = {(x, y) : x, y  R}
on this Set C define addition ‘+’ and multiplication ‘.’ by
(x1, y1) + (x2, y2) = (x1 + x2 , y1 + y2) → (1)
(x1, y1) . (x2, y2) = (x1 x2 – y1y2, x1y2 + x2y1) → (2)
Then the elements of C which satisfy the above rules of addition
and multiplication are called complex numbers. (2 marks)
Properties of addition1.
Closure law : If z1 = (x1,y1), z2 (x2, y2)
Then from Equation (1) z1+ z2 = (x1,y1) + (x2, y2) = (x1 + x2,
y1+y2)
Which is also ordered pair of real numbers. Hence z1+z2  C,
therefore for every z1, z2 C, z1+z2  C (2 marks)
2.
Associate law :
z1+(z2 + z3) = (z1+ z2) + z3 for every z1, z2, z3C (2 marks)
Similarly other any 3 properties can be explained.
Properties of multiplication1.
Closure law : If z1 = (x1, y1), z2 = (x2, y2)C then from (2)
(2 marks)
z1, z2 = (x1, y1) (x2, y2) = (x1x2 – y1y2, x1y2 + x2y1)
Which is also an ordered pair of real number. Hence z1, z2 is also a
complex number. Thus for every z1, z2C, z1z2C
2.
Existence of identity element :
There exists (1, 0) C such that (x, y)(1, 0) = (x.1 –y.0, x.0 + 1.y) =
(x, y) for every (x, y) C. Here (1, 0) is called the
multiplicative identity element. (2 marks)
Similarly other any three properties can be explained.