In the set of integers Z, exmine whether the following relations are equivalence relations or not : `R={(a,b) : a,b in Z and a>b}`

In the set of integers Z, exmine whether the following relations are equivalence relations or not : R={(a,b) : a,b in Z and ageb}

In the set of integers Z, examine whether the following relations are equivalence relations or not : R={(a,b) : a,b in Z and aleb}

In the set of integers Z, exmine whether the following relations are equivalence relations or not : R={(a,b) : a,b in Z and a^2=b^2}

State whether the following relations are reflexive, symmetric and transitive: R={(a,b) : a,b in Z and a+b is even } in the set of integers, Z.

Which.of the following relations are functions?f= {(a, x), (b, y), (c, z)}

Find whether the operation * is a binary operation or not on the given set : a**b=a^b on N

Find whether the operation * is a binary operation or not on the given set : a**b=|a-b| on Z.

Are the following relations true? If not, illustrate with examples. a(b+c) = ab + ac

Are the following relations true? If not, illustrate with examples. (a-b)+b =a

Show that the intersection of two equivalence relations in a set is again an equivalence relation in the set