For the relation `R_1` defined on `R` by the rule `(a ,b) in R_1:1+ab > 0.` Prove that: for`(a ,b) in R_1a n d(b ,c) in R_1 then (a ,c) in R_1` is not true for all `a ,b ,c in R`

For the binary operation * defined on R-{1} by the rule a * b=a+b+a b for all a ,\ b in R-{1} , the inverse of a is

Check whether the relation R_1 in R defined by R_1 = {(a,b): a leb^3) is reflexive, symmetric ?

Let R be a relation in N defined by R={(a , b); a , b in N\ a n d\ a=b^2dot} Are the following true: (i)\ (a , a) in R\ AA\ a in N (ii)\ (a , b) in R=>(b , a) in R (iii)\ (a , b) in R ,(b , c) in R=>(a , c) in R

Let R_(1) be a relation defined by R_(1)={(a,b)|agtb,a,b in R} . Then R_(1) , is

Let a relation R_1 on the set R of real numbers be defined as (a ,\ b) in R_1 1+a b >0 for all a ,\ b in R . Show that R_1 is reflexive and symmetric but not transitive.

Let a relation R_1 on the set R of real numbers be defined as (a , b) in R iff 1+a b >0 for all a , b in Rdot Show that R_1 is reflexive and symmetric but not transitive.

Prove that the relation R on the set NxxN defined by (a ,\ b)R\ (c ,\ d) a+d=b+c for all (a ,\ b),\ (c ,\ d) in NxxN is an equivalence relation. Also, find the equivalence classes [(2, 3)] and [(1, 3)].

Prove that r_(1) r_(2) + r_(2) r_(3) + r_(3) r_(1) = (1)/(4) (a + b + c)^(2)

Let R be a relation on NxxN defined by (a , b)\ R(c , d)hArra+d=b+c\ if\ (a , b),(c , d) in NxxN then show that: (i)\ (a , b)R\ (a , b)\ for\ a l l\ (a , b) in NxxN (ii)\ (a , b)R(c , d)=>(c , d)R(a , b)for\ a l l\ (a , b),\ (c , d) in NxxN (iii)\ (a , b)R\ (c , d)a n d\ (c , d)R(e ,f)=>(a , b)R(e ,f)\ for all \ (a , b),\ (c , d),\ (e ,f) in NxxN

Prove that (r_(1) -r)/(a) + (r_(2) -r)/(b) = (c)/(r_(3))