Set Theory, Number Systems, Relations, and Functions Questions | Prasnya
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Set Theory, Number Systems, Relations, and Functions - Set Theory, Number...
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Q1
In a survey among
250
250
students in Bandipur House of IITM BS degree, the following data were found:
100
100
students have a Spotify subscription,
110
110
students have a YouTube Premium subscription,
120
120
students have an Apple Music membership,
30
30
students have both Spotify and YouTube Premium subscriptions,
30
30
students have both Spotify and Apple Music subscriptions, and
40
40
students subscribe to both YouTube Premium and Apple Music. Assuming that every student has at least one subscription, determine how many students have memberships to all three platforms: Spotify, YouTube Premium, and Apple Music.
Integer answer
MARCH 15, 2026
MARCH 15, 2026
Q2
Let
R
=
{
(
a
,
c
)
,
(
b
,
c
)
,
(
d
,
c
)
,
(
b
,
a
)
}
R=\{(a,c),(b,c),(d,c),(b,a)\}
be a relation on the set
A
=
{
a
,
b
,
c
,
d
}
A=\{a,b,c,d\}
. Determine the correct properties of
R
R
.
Multiple correct
MARCH 15, 2026
MARCH 15, 2026
Q3
If
A
=
{
4
,
5
,
6
}
A=\{4,5,6\}
,
B
=
{
4
,
7
,
8
}
B=\{4,7,8\}
, and
C
=
{
4
,
6
,
7
}
C=\{4,6,7\}
, find the cardinality of
(
A
−
B
)
×
(
B
∩
C
)
(A-B)\times(B\cap C)
.
Integer answer
MARCH 15, 2026
MARCH 15, 2026
