Relations and Their Types Questions | Prasnya
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Week 1
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Relations and Their Types - Relations and Their Types
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Q1
An online degree programme offers the following courses: Level I: Mathematics, Statistics; Level II: Machine Learning Foundations, Mathematical Thinking; Level III: Deep Learning, Machine Learning Techniques, Advanced Algorithms. Every course in Level I is a prerequisite for every course in Level II, and every course in Level II is a prerequisite for every course in Level III. Let
M
M
be the set of all these courses and define two relations on
M
M
:
R
=
{
(
A
,
B
)
∣
A
R = \{(A, B) \mid A
and
B
B
are courses in the same level
}
\}
and
S
=
{
(
A
,
B
)
∣
A
S = \{(A, B) \mid A
is a prerequisite for
B
}
B\}
. Which of the following statements is/are correct?
Multiple correct
OCTOBER 26, 2025
OCTOBER 26, 2025
Q2
Consider a set
S
=
{
a
∣
a
∈
N
,
a
≤
10
}
S = \{a \mid a \in \mathbb{N},\, a \leq 10\}
. Let
R
1
R_1
and
R
2
R_2
be relations on
S
×
S
S \times S
defined as
R
1
=
{
(
x
,
y
)
∣
x
,
y
∈
S
,
y
=
3
x
}
R_1 = \{(x, y) \mid x, y \in S,\, y = 3x\}
and
R
2
=
{
(
x
,
y
)
∣
x
,
y
∈
S
,
y
=
x
2
}
R_2 = \{(x, y) \mid x, y \in S,\, y = x^2\}
. Find the cardinality of
R
1
∖
R
2
R_1 \setminus R_2
.
Integer answer
OCTOBER 26, 2025
OCTOBER 26, 2025
Q3
Suppose
A
A
is the set of odd positive integers less than or equal to 20, and
B
B
is the set of positive integers less than or equal to 30 which are divisible by 5. Consider the following relation from
A
A
to
B
B
:
R
1
=
{
(
a
,
b
)
∣
a
∈
A
,
b
∈
B
,
a
divides
b
}
R_1 = \{(a, b) \mid a \in A,\; b \in B,\; a \text{ divides } b\}
Which of the following statements is correct?
Single correct
JULY 13, 2025
JULY 13, 2025
Q4
The Cartesian product
A
×
A
A \times A
has 9 elements. Two of the elements of the Cartesian product are
(
1
,
3
)
(1, 3)
and
(
3
,
7
)
(3, 7)
. Find the sum of all the elements in set
A
A
.
Integer answer
FEBRUARY 23, 2025
FEBRUARY 23, 2025
Q5
Which of the following option(s) is/are true for the relation
R
1
=
{
(
x
,
y
)
:
x
,
y
∈
R
,
x
2
+
y
2
=
1
}
R_1 = \{(x, y) : x, y \in \mathbb{R},\; x^2 + y^2 = 1\}
?
Single correct
FEBRUARY 23, 2025
FEBRUARY 23, 2025
