Let `r` be relation from `R` (set of real numbers) to R defined by `r={(a,b)|a, b in R and a-b+sqrt3` isan irrational number}. The relation `r` is

Options

A. an equivalence relation
B. only reflexive
C. only symmetric
D. only transitive

Answer

B

Explanation

Given, `r={(a,b)|a,b in R" and "a-b+sqrt(3)" is an irrational number"}`
Reflexive `araAAainR," as"`
`a-a sqrt(3)=sqrt(3)` is an irrational number.
`implies" r is reflexive."`
Symmetric `sqrt(3)r2," as"` brgt `sqrt(3)-2+sqrt(3)=2sqrt(3)-2` is an irrational number but `2rsqrt(3)`, as `2-sqrt(3)+sqrt(3)=2` is not an irrational number.
`:.` r is not symmetric.
Transitive `2r2sqrt(3)" and "2sqrt(3)rsqrt(3)" but "2rsqrt(3)`
`:.` r is not transitive.