Let R Nk be a k-ary relation. Say that R is denable in

Chapter , Problem 6.28

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Let R Nk be a k-ary relation. Say that R is denable in Th(N,+) if we can give a formula with k free variables x1,...,xk such that for all a1,...,ak N, (a1,...,ak) is true exactly when a1,...,ak R. Show that each of the following relations is denable in Th(N,+). Aa. R0 = {0} b. R1 = {1} c. R= = {(a,a)| a N} d. R< = {(a,b)| a,b N and a < b}