Let S be the subset of the set of ordered pairs of integers defined recursively by: Base case: (0, 0) ∈ S Recursive step: If (a, b) ∈ S, then (a + 1, b + 3) ∈ S and (a + 3, b + 1) ∈ S. (1) List the elements of S produced by the first four applications of the recursive definition (this should produce 14 new elements).
(2) Use structural induction to show for all (a, b) ∈ S that (a+b).

Problem situation: caren is making rice and beans. she can spend no more than $10 on ingredients. she buys one bag of rice for $4.99. beans cost $0.74 per pound. how many pounds of beans, x, can she buy? inequality that represents this situation: 10≥4.99+0.74x drag each number to show if it is a solution to both the inequality and the problem situation, to the inequality only, or if it is not a solution.