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
EXAM MAP
Medical
NEET