Let S be the set of all real numbers and let R be a relation in s,defined by `R={(a,b):aleB^(2)}.` show that R satisfies none of reflexivity , symmetry and transitivity .

Let S be the set of all real numbers and let R be a relation in s,defi

1.	Let S be the set of all real numbers and let R be a relation in s,defined by `R={(a,b):aleB^(2)}.` show that R satisfies none of reflexivity , symmetry and transitivity .
Answer» (i) Nonreflexivity Clearly ,`(1)/(2)` is a real number and `(1)/(2)le ((1)/(2))^(2)` is not true . `therefore ((1)/(2),(1)/(2))!in R.` hence ,R is not reflexive . (ii) Nonsymmetry consider the real numbers `(1)/(2) and 1.` Clearly ,`(1)/(2)le a^(2) implies((1)/(2),1)in R` but ,`1le((1)/(2))^(2)` is not true and so `(1,(1)/(2))!in R.` thus `((1)/(2),1)in R` but` (1,(1)/(2))in R.` hence ,R is not symmetric . (iii) Nontransitivity consider the real numbers 2,-2 and 1. Clearly `2le(-2)^(2)and -2le (1)^(2)"but" 2lt1^(2)`is not true . thus ,`(2,-2)in R and (-2,1)in R`but `(2,1)in R.` hence R is not transitive .

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Let S be the set of all real numbers and let R be a relation in s,defined by `R={(a,b):aleB^(2)}.` show that R satisfies none of reflexivity , symmetry and transitivity .

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