GATE CSE 2019 | Set Theory & Algebra Question 11 | Discrete Mathematics

GATE CSE 2019

MCQ (Single Correct Answer)

-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?

R₁ only

Neither R₁ nor R₂

R₁ and R₂

R₂ only

GATE CSE 2019

MCQ (Single Correct Answer)

-0.33

Let U = {1, 2 ,..., n}. Let A = {(x, X) | x ∈ X, X ⊆ U}. Consider the following two statements on |A|.

I. |A| = n2^n–1

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

Which of the above statements is/are TRUE?

Neither I nor II

Only II

Both I and II

Only I

GATE CSE 2015 Set 3

MCQ (Single Correct Answer)

-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?

$$\forall X \in U\,\,$$ $$\left( {\left| X \right| = \left| {X'} \right|} \right)$$

$$\exists X \in U$$ $$\exists Y \in U\,\,$$ $$\left( {\left| X \right| = 5,\left| Y \right| = 5} \right.$$ and $$\left. {X \cap Y = \phi } \right)$$

$$\forall X \in U\,$$ $$\forall Y \in U\,\,$$ $$\,\,\left( {\left| X \right| = 2,\left| Y \right| = 3{\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} and{\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} X\backslash Y = \phi } \right)$$

$$\forall X \in U\,\,$$ $$\forall Y \in U\,\,$$ $$\,\left( {X\backslash Y = Y'\backslash X'} \right)$$

GATE CSE 2015 Set 2

Numerical

-0

The cardinally of the power set of $$\left\{ {0,1,2,\,\,....,\,\,10} \right.\left. \, \right\}$$ is _____________.

Your input ____