Question 6.28: Let R ⊆ N^k be a k-ary relation. Say that R is definable in ...

Let R \subseteq N^{k} be a k-ary relation. Say that R is definable in Th(N,+) if we can give a formula \phi with k free variables x_{1}, . . . ,x_{k} such that for all a_{1}, . . . ,a_{k} \in N, \phi (a_{1}, . . . ,a_{k}) is true exactly when a_{1}, . . . ,a_{k}\in R. Show that each of the following relations is definable in Th(N,+).
a. R_{0} = {0}

c. R_{=} = {(a, a) | a ∈ N}