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

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}

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.

Give examples of two relations such that one is an equivalence relation and the other is not.

State whether the following relations are reflexive, symmetric and transitive: R={(x,y) : x,y in A, y is divisible by x} in the set A={1,2,3,4,5,6,7,8,}