EXERCISE 3.1.2: Valid and invalid arguments in English. Which of the following arguments are invalid and which are valid? Prove your answer by replacing each proposition with a variable to obtain the form of the argument. Then prove that the form is valid or invalid. The patient has high blood pressure or diabetes or both. The patient has diabetes or high cholesterol or both (a) The patient has high blood pressure or high cholesterol. He studied for the test or he failed the test or both (b) He passed the test. .:. He studied for the test. If v2 is an irrational number, then 2/2 is an irrational number 2v/2 is an irrational number (c) 2 is an irrational number