Ques. -2

Algebra Level 4

The relation R = { ( 1 , 1 ) , ( 2 , 2 ) , ( 3 , 3 ) , ( 1 , 2 ) , ( 2 , 3 ) , ( 1 , 3 ) } R=\{ (1,1),(2,2),(3,3),(1,2),(2,3),(1,3) \} on the set A = { 1 , 2 , 3 } A=\{1,2,3 \} is:

reflexive but not transitive neither symmetric nor transitive reflexive but not symmetric symmetric and transitive

Sandeep Bhardwaj by Sandeep Bhardwaj , 28, India

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1 solution

Saurabh Patil
Apr 18, 2015

Reflexive property is said to be present in set if ( a , b ) and ( b , a ) are the part of that set.Where a , b can be any quantity ( real / complex number etc. )

Symmetric property is present in a set for those which contain the element ( a , b ) such that a = b .

Transitive property is present in a set if (a , b ) , ( b , c ) are a part of set then there should also exist ( a , c )

As here the set contains ( 1 , 1 ),(2 , 2 ), (3 , 3 ), ( 1 , 2 ), (2 , 3 ), (1 , 3 ), so the set is transitive and reflexive but not symmetric.

NOTE : If a set follows all the three property ( Stated above ), then the set is said to be following an Equivalence relation

2 Helpful 0 Interesting 0 Brilliant 0 Confused

(1,2) is in the set but (2,1) isn't in the set, so why is it reflexive?

Kelvin Hong - 3 years ago

Reflexive relations are ones for which ( a , a ) ∈ R (a,a) \in R for all a a . Symmetric ones are ones for which ( b , a ) ∈ R (b,a) \in R whenever ( a , b ) ∈ R (a,b) \in R . You have the definititions of these two back to front. This relation is reflexive and transitive, but not symmetric.

N.B. This relation is simply ≤ \le .

Mark Hennings - 3 years ago

1 pending report

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