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

The relation R defined in the set A={-1,0,1} as R={(a,b):a=b^2} Chech whether R is reflexive, symmetric and transitive.

Let R be a Relation in the set A={1,2,3,4,5,6} define as R={(x,y):y=2x-1} Is R an equivalance relation? Justify.

The relation R defined on the A={-1,0,1} as R={(a,b):a^2=b} Check whether R is reflexive,symmetric and transitive

Show that each of the relation R in the set A={x in Z: 0lt= xlt=12} ,given by R = {(a,b) : a=b} is an equivalence relation. Find the set of all elements related to 1 in each case.

Check whether the relation R defined in the set {1,2,3,4,5,6} as R={(a,b) : b=a+1} is reflexive, symmetric or transitive.

Show that the relation R in the set A = (1,2,3,4,5} given by R = {(a,b) : |a - b| is even }, is an equivalence relation. Show that all the elements of {1,3,5} are related to each other and all the elements of {2,4} are related to each other. But no element of {1, 3, 5} is related to any element of {2,4}.

Let f: X rarr Y , be a function. Define a relation R in X given by: R={(a, b): f(a)=f(b)} Examine if R is an equivalence relation.

Show that the relation R in the set R of real number, defined as R = {(a.b): a lt= b^2} is neither reflexive nor symmetric nor transitive.

Show that the relation R in the set R of Real numbers defined as R={(a,b):aleb^2} is neither reflexive, nor symmetric, nor transitive.

Show that the relation R in the set is given by A={x in Z,0lexle12} R={(a,b):a-b is a multiple of 4} is an equivalence relation.