Let s be the subset of the set of ordered pairs of integers defined recursively by: basis step: (0, 0) ∈ s. recursive step: if (a, b) ∈ s, then (a, b + 1) ∈ s, (a + 1, b + 1) ∈ s, and (a + 2, b + 1) ∈ s. a) list the elements of s produced by the first four applications of the recursive definition. b) use strong induction on the number of applications of the recursive step of the definition to show that a ≤ 2b whenever (a, b) ∈ s. c) use structural induction to show that a ≤ 2b whenever (a, b) ∈ s.

Which expressions are equivalent to -6 + 3m

Barbara has a good credit history and is able to purchase a car with a low-interest car loan. she co-signs a car loan for her friend jen, who has poor credit history. then, jen defaults on the loan. who will be held legally responsible by the finance company and why? select the best answer from the choices provided. a. barbara will be held legally responsible because she has a good credit history. b. jen will be held legally responsible because she drives the car. c. barbara will be held legally responsible because she is the co-signer. d. jen will be held legally responsible because she has a poor credit history. the answer is a

What is the probability of throwing several dice with sum equal to 6 (six)? show the ways of possibilities for sum 6 (as the numerator) and the ways of throwing n dices for n = 1, 2, 3, 4 or 5 as denominator for all the questions to earn full credits. (a)throw one die, (b) throw two dice, (c) throw three dice (d) throw 4 dice, (e) throw 5 dice