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, exmine whether the following relations are equivalence relations or not : R={(a,b) : a,b in Z and a

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, 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-b is divisible by 2.

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}

Examine whether the following functions are one-one or not : f : Z rarr Z, f(x) = x^2+5

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)}

State whether the following sets are null set or singleton set: {x|x in R,x!=x}

State whether the following sets are null set or singleton set: {x|x in R,x^2=-4}