in Set Theory & Algebra
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1 vote
1 vote

A relation $R$ is defined as $xRy$ , if $x$ and $y$ are NOT equal. This relation $R$ is

  1. symmetric but not reflexive
  2. symmetric and transitive but not reflexive
  3. an equivalent relation
  4. none of reflexive or symmetric or transitive
in Set Theory & Algebra
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2 Comments

Why option a is correct pls explain
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@kavita_joshi

xRy and yRx then xRx so it is not  transitive .

read this slide -->  http://www3.cs.stonybrook.edu/~pfodor/courses/CSE215/L14-Relations.pdf

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3 Answers

3 votes
3 votes

relation hold iff x!=y

1 :for reflexive: xRx  (x!=x) false ;

2: for symmetric xRy=yRx ( x!=y and y!=x )  true

3: for transitive lets : (x,y)=(1,2) (y,z) =(21) (x,z)=(11)

here xRy ,yRz hold but xRx doesn't (as 1=1 )

2 Comments

So , a fact can be derived that every transitive relation is reflexive also.

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 That is incorrect.

$A=\left \{1,2,3 \right \}$

Relation R on A = $A=\left \{(1,2) ,(2,1), (1,1) \right \}$

Transitive but not reflexive.

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0 votes
0 votes
I believe option is B , since it is transitive as well .
Why is the answer A ?
by

1 comment

xRy and yRx then xRx so it won't be transitive
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0 votes
0 votes
  • Can't be reflexive.

     
  • Symmetric, yes. Because if xRy then yRx.

     
  • Transitive? Let's see. if xRy and yRz then xRz. True.

    if xRy and yRx then xRx... So, not transitive as xRx doesn't belong to the "not equal to" relation.

Option A

Answer:

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