Show that the `vv: R ->R` given by `(a , b)->m a x {a , b}`and the `^^: R ->R``->`given by `(a , b) ->m in {a , b)`are binary operations.

Show that the quad vv:R rarr R given by and the and the given by quad (a,b)rarr min{a,b) are binary operations.

Show that quad *:R xx R rarr R given by (a,b)rarr a+4b^(2) is a binary operation.

Let *R*R^(rarr) given by (a,b)vec a+4b^(2) is a binary operation.Compute (-5)*2*0)

Show that *:R xx R rarr R given by a*b=a+2b is not associative.

Show that the relation R in R defined as R={(a,b):ageb} is transitive.

Show that the function f:R rarr given by f(x)=xa+b, where a,b in R,a!=0 is a bijection.

Let A be the set of all students of a boys school. Show that the relation R in A given by R = {(a, b) : a is sister of b} is the empty relation and R^(prime) = {(a, b) : the difference between heights of a and b is less than 3 meters} is the un

Show that the operation vv and ^^ on R defined as a vv b= Maximum of a and ba^^b= Minimum of a and b are binary operations of R.

Let R be a relation on the set N given by R={(a ,\ b): a=b-2,\ b >6}dot Then, (2,\ 4) in R (b) (3,\ 8) in R (c) (6,\ 8) in R (d) (8,\ 7) in R

Let R be the relation in the set N given by R = {a,b):a is a multiple of b} .Then :