Write each of the following arguments in argument form. Then, use the rules of inference to...

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Write each of the following arguments in argument form. Then, use the rules of inference to show that each argument is valid. a. Let p be "it snows," q be "I take the subway," and r be "I am late for class." I take the subway when it snows. If I take the subway, then I am late for class. I was not late for class. Therefore, it did not snow. b. Let P(x) be "x attended the lecture," Q(x) be "x submitted the homework assignment," and R(x) be "x passed the exam," where the domain consists of all students in this class. Every student in this class who did not attend the lecture or did not submit the homework assignment did not pass the exam. Bob, who is a student in this class, passed the exam. Therefore, Bob attended the lecture. Write each of the following arguments in argument form. Then, use the rules of inference to show that each argument is valid. a. Let p be "it snows," q be "I take the subway," and r be "I am late for class." I take the subway when it snows. If I take the subway, then I am late for class. I was not late for class. Therefore, it did not snow. b. Let P(x) be "x attended the lecture," Q(x) be "x submitted the homework assignment," and R(x) be "x passed the exam," where the domain consists of all students in this class. Every student in this class who did not attend the lecture or did not submit the homework assignment did not pass the exam. Bob, who is a student in this class, passed the exam. Therefore, Bob attended the lecture.