roblem 1 [20 points] Let P be a domain of (set of) products, and D be a domain of days. Use the functions sale (p,d): returns sales amount of product p on day d next(d) : returns the day after day d and the predicate Stock (p,d) : returns true if product p is available in stock on day d to translate the following sentences into predicate logic. Important Note. Your formalization will only be correct if you have understood the sentences correctly. If you are unsure about the intended meaning of a sentence, please ask for clarification. (a) (2 points) There exists a day such that the sum of the sales amounts of product p1,p2, and p3 is equal to 10. (b) (2 points) Days on which product p1 has sales. (c) (2 points) Days on which no product has sales. (d) (2 points) A product can not be sold if it is not available. (e) (2 points) Every day, there are some products whose sales are not less than all other products. (f) (2 points) All days on which product p5 had the largest sales amount of all products on that day. (g) (2 points) There exist a product with a sales amount over 7 for exactly 2 consecutive days. (h) (2 points) There exists a product with monotonically increasing sales. "i.e., there exists a product such that its sales on any day are greater than its sales on the previous days." (i) (2 points) Every day has only one top selling product. "i.e., every day has exactly one product whose sales amount on that day is the largest of all products." (j) (2 points) Products with two days without any sales