CUSTOMER_CODE
SMUDE
DIVISION_CODE
SMUDE
EVENT_CODE
OCTOBER15
ASSESSMENT_CODE MCA1030_OCTOBER15
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
74005
Explain the concept of Logical Equivalence with example.
QUESTION_TEXT
SCHEME OF
EVALUATION
Solution:
Two statements S1(p, q, r, …) and S2 (p, q, r, …) are said to be logically
equivalent, or simply equivalent if they have the same truth values for
all logical possibilities and is denoted by
S1(p, q, r, …) = S2 (p, q, r, …)
In other words, S1 and S2 are logically equivalent if they have identical
truth tables (by identical truth tables we mean the entries in the last
column of the truth tables are same.
(4 marks)
Example: Show that ~(p^q) is logically equivalent to (~p)v(~q)
(6 marks)
Solution: The truth tables for both the statements are
Truth table for ~(p^q)
p q (p^q) ~(p^q)
T T T
F
T F F
T
F T F
T
F F F
T
Truth table for (~p)v(~q)
p q ~p ~q (~p)v(~q)
T T F F
F
T F F T
T
F T T F
T
F F T T
T
Now, observe that the entries (truth values) in the last column of both
the tables are same. Hence, the statement ~(p^q) is equivalent to the
statement (~p)v(~q)
QUESTION_TYPE
DESCRIPTIVE_QUESTION
QUESTION_ID
124970
QUESTION_TEXT
Explain the concepts of scalar and vector field with example.
SCHEME OF EVALUATION
(5 marks each)
QUESTION_TYPE
DESCRIPTIVE_QUESTION
QUESTION_ID
124973
QUESTION_TEXT
SCHEME OF
EVALUATION
Explain the following with example:
i.
Disjunction
ii. Negation
iii. Truth table
Disjunction
If two simple statements p and q are connected by the word ‘or’,
then the resulting compound statement “p or q” is called disjunction
of statements p and q
Example: Form the disjunction of the following simple statements:
p : The sun shines.
q :It rains.
Solution: The disjunction of the statements p and q is given by
pν q : The sun shines or it rains.
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.
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)
SCHEME OF
EVALUATION
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.