Suppose () and () are statements that depend on a natural number . You are given that some statements and implications are true. Which of these properties imply that () is true for every natural number 1?

(1 point) Suppose P(n) and S (n) are statements that depend on a natural number n. You are given that some statements and implications are true. Which of these properties imply that P(n) is true for every natural number n 2 1? v 1. P(1), P(k) : S(k + 1), and S(k) : P(k + 1) for all k 2 1 v 2. P(1), P(3), P(S), P(k) : P(k + 6), and P(k) : P(2k) for all k z 1 v 3. P(1), 5(1), P(k) : S(k + 1), P(k) :. S(k + 2) and S(k) : P(k + 1) for all k 2 1 v 4. P(1), P(2), P(k) : P(k + 2), and P(k) : P(k + 3) for all k z 1 v 5. P(1), P(k +1) : P(k), and P(k) : P(2k) for all k z 1 v 6. P(1), S(l), P(k) S(k +1), P(k) Q S(k + 2) and S(k) 3 P(k + 2) for all k 2 1