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Question

Let S={1,2,3,4,5} and let A=S×S. Define the relation R on A as follows (a,b)R(c,d) if and only if ad=cb. Then R is

A
Reflexive only
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B
symmetric only
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C
Transitive only
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D
Equivalence relation
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Solution

The correct options are
A Reflexive only
D symmetric only
Given tha S=1,2,3,4,5 and A=S×S
A relation R on A is defined as follows :"(a,b)R(c,d)" if and only if ad=cd
(i) R is reflexive, since ab=ab, therefore, (a,a)R(b,b)a,bS
(ii) R is symmetric, since (a,b)R (b,a)Ra,bS
(iii) R is not transitive (a,b),(b,c)R doesnot necessarily imply (a,c) belongs to R

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