Is ( (P→Q) ˄ Q ) → P true or false? You need to prove your answer

Suppose f(n) = O(F(n)) and g(n) = O(G(n)). Is it true that f(n) / g(n) = O(F(n) / G(n))? Provide a proof using the definition of big-oh, or provide values for the four functions as a counterexample.

7. For n 2 1, in how many out of the n! permutations T = (T(1), 7(2),..., 7 (n)) of the numbers {1, 2, ..., n} the value of 7(i) is either i – 1, or i, or i +1 for all 1 < i < n? Example: The permutation (21354) follows the rules while the permutation (21534) does not because 7(3) = 5. Hint: Find the answer for small n by checking all the permutations and then find the recursive formula depending on the possible values for 1(n).

Please answer it asap. both questions.