1.

LetR be the real line. Consider the following subsets of the plane `RxxR`.`S""=""{(x ,""y)"":""y""=""x""+""1""a n d""0""

Answer» Correct Answer - C
`T={(x,y):x-yinI}`
As `0 in I`, so T is a reflexive relation
If `x-yinIimpliesy-x inI`
`therefore` T is symmetric also.
If x - y = I and y - z = 12
Then, `x-z=(x-y)+(y-z)=I_(1)+I_(2)inI`
`therefore` T is also transitive.
Hence, T is an equivalence relation. Clearly, `xnex+1implies(x,x)cancelinS`
`thereforeS` is not reflexive.


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