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 relation R_(1) defined on R by the rule (a,b)in R_(1):1+ab>0. Prove that: for (a,b)in R_(1)and(b,c)in R_(1)then(a,c)in R_(1) is not true for all a,b,c in R

A relation R_(1) is defined on the set of real numbers as follows: (a,b) in R_(1) hArr 1 + ab gt 0 , when a, b in R (iii) (a,b) in R_(1) and (b,c) in R_(1) rarr (a,c) in R_(1) is not true when 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

For the binary operation * defined on R-{-1} by the rule a*b=a+b+ab for all a,b in R-{1}, the inverse of a is a (b) -(a)/(a+1)(c)(1)/(a) (d) a^(2)

The relation R defined in the set A={-1,0,1} as R={(a,b):a=b^2} Is R an equivalance relation

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 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

Prove that sum (r+r_1) tan ((B-C)/( 2))=0