Write each of these statements in the form “if 𝑝, then 𝑞” in English.a) I will remember to send you the address only if you send me an e-mail message.b) To be a citizen of this country, it is sufficient that you were born in the United States.c) If you keep your textbook, it will be a useful reference in your future courses.d) The Red Wings will win the Stanley Cup if their goalie plays well.e) That you get the job implies that you had the best credentials.f) The beach erodes whenever there is a storm.g) It is necessary to have a valid password to log on to the server.h) You will reach the summit unless you begin your climb too late.

Write each of these statements in the form “if 𝑝, then 𝑞” in English.a) He gets sick whenever the weather gets cold. (1 POINT)b) It is necessary to wake up early to beat today’s traffic. (1 POINT)c) A positive integer is a prime only if it has no divisors other than 1 and itself.(1 POINT)d) John will go to Dubai during the mid-semester break unless he runs out of money

Required informationSkip to questionNOTE: This is a multi-part question. Once an answer is submitted, you will be unable to return to this part.Write the given sentence in the "if p, then q" form.The Red Wings will win the Stanley Cup if their goalie plays well.Multiple ChoiceIf their goalie plays well, then the Red Wings will lose the Stanley Cup.If the Red Wings win the Stanley Cup, then their goalie did not play well.If their goalie plays well, then the Red Wings will win the Stanley Cup.If the Red Wings win the Stanley Cup, then their goalie played well.If the Red Wings lose the Stanley Cup, then their goalie played well.

Let 𝑃(𝑥, 𝑦) be the statement “𝑥 enjoys playing 𝑦,” where the domain for𝑥 consists of all Ashesi students and that of 𝑦 consists of all sports.Express each of these statements by a simple English sentence.a) 𝑃(Paul, football)b) ∃𝑦𝑃(Carol, 𝑦)c) ∃𝑥(𝑃(𝑥, basketball) ∧ 𝑃(𝑥, badminton))d) ∃𝑥∀𝑦((𝑥 ≠Ben) ∧ (𝑃(Ben, 𝑦) → 𝑃(𝑥, 𝑦))

Exercise 6: (5 POINTS) Suppose the variable 𝑥 represents students and 𝑦 represents courses,and:𝐴(𝑥): 𝑥 is a part-time student𝑀(𝑦): 𝑦 is a math course𝐹(𝑥): 𝑥 is a freshman𝐵(𝑥): 𝑥 is a full-time student𝑇(𝑥, 𝑦): student 𝑥 is taking course 𝑦.1. Write the following statements using these predicates and any needed quantifiers.a) Caroline is not taking any course. (1 POINT)b) No student is taking every course. (1 POINT)2. Write the following statements in good English without using variables in your answers.a) ∃𝑦∀𝑥[𝐴(𝑥) → 𝑇(𝑥, 𝑦)] (1 POINT)b) ∀𝑥∃𝑦[(𝐵(𝑥) ∧ 𝐹(𝑥)) → (𝑀(𝑦) ∧ 𝑇(𝑥, 𝑦))] (2 POINTS)

Suppose the variable 𝑥 represents students and 𝑦 represents courses,and:𝐴(𝑥): 𝑥 is a part-time student𝑀(𝑦): 𝑦 is a math course𝐹(𝑥): 𝑥 is a freshman𝐵(𝑥): 𝑥 is a full-time student𝑇(𝑥, 𝑦): student 𝑥 is taking course 𝑦.1. Write the following statements using these predicates and any needed quantifiers.a) Caroline is not taking any course. (1 POINT)b) No student is taking every course. (1 POINT)2. Write the following statements in good English without using variables in your answers.a) ∃𝑦∀𝑥[𝐴(𝑥) → 𝑇(𝑥, 𝑦)] (1 POINT)b) ∀𝑥∃𝑦[(𝐵(𝑥) ∧ 𝐹(𝑥)) → (𝑀(𝑦) ∧ 𝑇(𝑥, 𝑦))]