Here are the types of questions that will be on Exam 2. As with Exam 1, you will not be using Submit or the Grade Grinder at all for this exam. Also, there will not be any “nested” quantifiers of the kind that we are starting to study in Chapter 11. (Nested quantifiers are where one quantifier appears within the scope of another quantifier.) Note that the problems start at “I,” picking up where we left off at the end of Exam 1 on Problem H.

Take Home Portion

(Circulated by email on Friday, Nov. 10, due by the beginning of class on Monday, Nov. 13) 75 pts total.

I. Here are five English sentences involving conditionals, biconditionals, and/or quantifiers. Translate them into FOL in a Tarski’s World sentence file. (25 pts)

J. Here are three FOL sentences involving conditionals, biconditionals, and/or quantifiers. Translate them into smooth, plain English, writing out your answers by hand or typing them up. (15 pts)

K. Here is a valid argument involving conditionals and/or biconditionals. Construct a proof of it using Fitch. You will not be permitted to use any of the “Con” rules. (25 pts)

L. Here is an argument that is Logically Valid, but First Order Invalid. Construct a FO-Counterexample that demonstrates this fact, writing out your answer by hand or typing it up. (10 pts)

In-Class Portion

(Administered in class on Monday, Nov. 13) 175 pts total.

M. Here is a valid argument or theorem involving conditionals and/or biconditionals. Construct a proof of it in Fitch. You will not need, and are not permitted to use, any of the “Con” rules. (40 pts)

N. Here are five sentences in English, involving conditionals, biconditionals, and/or quantifiers. Translate them into FOL in a Tarski’s World sentence file. (40 pts)

O. Here are five sentences in FOL involving quantifiers and/or conditionals/biconditionals. Translate them into smooth, plain English. (40 pts)

P. Here are four sentences. For each one, present its truth functional form and its FO form (using the nonsense replacement method). Then say what type of necessity each sentence involves. Is it (i) TT-necessary, (ii) FO-necessary but not TT-necessary, or (iii) Logically necessary but not FO-necessary? (40 pts)

Q. Short Answer Question(s) (15 pts)