Exam 17: The Logic of Declarative Statements

Figure out "Who ate the Pizza?" and explain the answer. The Puzzle: Five roommates, Abe, Bob, Carl, Dave, and Ziggy, share an off-campus apartment. On Monday night they had leftover pizza and so they put it in the refrigerator. On Tuesday when Ziggy went to get some of that pizza he found that it had all been eaten. Later Ziggy confronted his four roommates to find out who ate the pizza. Each roommate made one statement. The person who ate the pizza lied; his statement is false. The other three statements are true. Which one ate the pizza? Here are their four statements: Abe: I was in class all day. Bob: Carl ate the pizza. Carl: Bob's statement is false. David: Carl's statement is true.

Statements A and statement B are __________________ in the Logic of Statements if A and B have the same truth value under every interpretation of their statement letters.

Accurately and elegantly translate ((p → s) & (s → t)). Use these interpretations of the statement letters: p = "My son has chickenpox." q = "I have to stay home from work." r = "I need to take care of my son." s = "My son is contagious." t = "I need to call my boss."

Which of the following is the best translation of "If Lauren had not borrowed my car, then she would not have made it back to campus in time."

We can interpret the truth table below to be a demonstration that (q & p) and (p & q) are related to each other in what way(s)? p q (p\&q) (q\&p) ((p\&q)\rightarrow(q\&p)) ((q\&p)\rightarrow(p\&q)) T T T T T T T F F F T T F T F F T T F F F F T T

Construct the truth table for ((~(r → p) v (~p → r)) v q). Based on the truth table, correctly characterize the formula as tautology, inconsistent, or contingent. Explain the basis for the characterization.

Explain why an argument may fail to be valid at the level of the Logic of Statements, but might be discovered to be valid a deeper analytical level. The Logic of Statements is valuable for determining that a certain set of arguments is valid provided that the validity depends on the grammatical relationships between simple statements. But, as we saw in the chapter entitled "Valid Inferences," the validity of some arguments depends on relationships among classes of objects and their members, and it gives examples of valid inferences based on relationships between individuals, such as transitivity and reflexivity. The examples in those sections of that chapter would not be valid in the Logic of Statements.

Which of the following is the best description of an inconsistent statement in the Logic of Statements? "A grammatically correct expression ___________________.

How should the formula in the right most column of this truth table be characterized? p q r -p (r\rightarrowp) -(r\rightarrowp) (-p\rightarrowr) (-(r\rightarrowp)v(-p\rightarrowr)) ((-(r\rightarrowp)v(-p\rightarrowr))vq) 1 T T T F T F T T T 2 T T F F T F T T T 3 T F T F T F T T T 4 T F F F T F T T T 5 F T T T F T T T T 6 F T F T T F F F T 7 F F T T F T T T T 8 F F F T T F F F F

If a natural language statement is translated into symbolic logic and its truth table ends up with a T on at least one row and an F on at least one row, then the statement can be characterized as _____________.

Given two statements, A and B, we can say that A is equivalent to B in the Logic of Statements provided that ___________________.

Given two statements, A and B, we can say that A implies B in the Logic of Statements provided that ___________________.

In the Logic of Statements means a grammatically correct expression that turns out to be uncorrect under every possible assignment of truth values to its component simple statements is called inconsistent or ______________.

Which of the following is a conjunction?

At the level of the Logic of Statements, a tautology is implied by any statement and an inconsistent statement implies any statement. Moreover, any two tautologies or any two self-contradictory statements are equivalent. With regard to implication and equivalence, how should we resolve the differences between the treatment of these concepts in the Logic of Statements and how these same concepts apply in everyday real-world discourse?

Which of the following is the negation of a disjunction?

Which of the following is the best description of contingent statement in the Logic of Statements? "A grammatically correct expression ___________________.

Analyze the logic relationship called Disjunction and diagram a "Logic Circuit" with a power source and a light bulb that shows the conditions under which the light will be lit and not lit.

Two statements are equivalent at the level of the Logic of Statements if the bi-conditional of the two is a tautology.

Using "only if" compose a conditional in English from these two simple statements: "We took Grandfather's advice." And "We had a great time." Let the first one be "p" and the second by "q" and translate the conjunction into symbolic logic.