1
GATE CSE 2020
Numerical
+1
-0.33
Let R be the set of all binary relations on the set {1,2,3}. Suppose a relation is chosen from R at random. The probability that the chosen relation is reflexive (round off to 3 decimal places) is _____.
2
GATE CSE 2019
+1
-0.33
Let G be an arbitrary group. Consider the following relations on G :

R1: ∀a,b ∈ G, aR1b if and only if ∃g ∈ G such that a = g-1bg

R2: ∀a,b ∈ G, aR2b if and only if a = b-1

Which of the above is/are equivalence relation/relations?
A
R1 only
B
Neither R1 nor R2
C
R1 and R2
D
R2 only
3
GATE CSE 2019
+1
-0.33
Let U = {1, 2 ,..., n}. Let A = {(x, X) | x ∈ X, X ⊆ U}. Consider the following two statements on |A|.

I. |A| = n2n–1

II. |A| = $$\sum\limits_{k = 1}^n {k\left( {\matrix{ n \cr k \cr } } \right)}$$

Which of the above statements is/are TRUE?
A
Neither I nor II
B
Only II
C
Both I and II
D
Only I
4
GATE CSE 2015 Set 3
+1
-0.3
Suppose $$𝑈$$ is the power set of the set $$S = \left\{ {1,2,3,4,5,6,} \right\}$$. For any $$T \in U,$$ let $$\left| T \right|$$ denote the number of elements in $$𝑇$$ and $$T'$$ denote the complement of $$𝑇.$$ For any $$T,R \in U,$$ let $$T\backslash R$$ be the set of all elements in $$𝑇$$ which are not in $$𝑅.$$ Which one of the following is true?
A
$$\forall X \in U\,\,$$ $$\left( {\left| X \right| = \left| {X'} \right|} \right)$$
B
$$\exists X \in U$$ $$\exists Y \in U\,\,$$ $$\left( {\left| X \right| = 5,\left| Y \right| = 5} \right.$$ and $$\left. {X \cap Y = \phi } \right)$$
C
$$\forall X \in U\,$$ $$\forall Y \in U\,\,$$ $$\,\,\left( {\left| X \right| = 2,\left| Y \right| = 3{\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} and{\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} X\backslash Y = \phi } \right)$$
D
$$\forall X \in U\,\,$$ $$\forall Y \in U\,\,$$ $$\,\left( {X\backslash Y = Y'\backslash X'} \right)$$
GATE CSE Subjects
Discrete Mathematics
Programming Languages
Theory of Computation
Operating Systems
Digital Logic
Computer Organization
Database Management System
Data Structures
Computer Networks
Algorithms
Compiler Design
Software Engineering
Web Technologies
General Aptitude
EXAM MAP
Joint Entrance Examination