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 _____.

Your input ____

2

GATE CSE 2019

MCQ (Single Correct Answer)

+1

-0.33

Let G be an arbitrary group. Consider the following relations on G :

R1: ∀a,b ∈ G, aR

R2: ∀a,b ∈ G, aR

Which of the above is/are equivalence relation/relations?

R1: ∀a,b ∈ G, aR

_{1}b if and only if ∃g ∈ G such that a = g^{-1}bgR2: ∀a,b ∈ G, aR

_{2}b if and only if a = b^{-1}Which of the above is/are equivalence relation/relations?

3

GATE CSE 2019

MCQ (Single Correct Answer)

+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| = n2

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

Which of the above statements is/are TRUE?

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?

4

GATE CSE 2015 Set 3

MCQ (Single Correct Answer)

+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?

Questions Asked from Set Theory & Algebra (Marks 1)

Number in Brackets after Paper Indicates No. of Questions

GATE CSE 2024 Set 2 (1)
GATE CSE 2024 Set 1 (2)
GATE CSE 2020 (2)
GATE CSE 2019 (2)
GATE CSE 2015 Set 3 (1)
GATE CSE 2015 Set 2 (2)
GATE CSE 2015 Set 1 (1)
GATE CSE 2014 Set 3 (1)
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GATE CSE 2009 (2)
GATE CSE 2008 (1)
GATE CSE 2007 (2)
GATE CSE 2006 (4)
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GATE CSE 1998 (3)
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GATE CSE 1995 (2)
GATE CSE 1993 (2)
GATE CSE 1987 (2)

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