Exam 17: The Logic of Declarative Statements

The truth table below demonstrates that the argument "(q v r) and ~r, so therefore q" is ___________________. q r (qvr) -r ((qvr)\&-r) (((qvr)\&-r)\rightarrowq) T T T F F T T F T T T T F T F F F T F F T T F T

Which of the following is a grammatically correct formula of declarative logic?

Consider this argument: "If we buy tickets online, then we save money. If we ask for the student discount, then we save money. We did not ask for the student discount, but we did buy tickets online. So we saved money." Using a truth table to evaluate that argument for validity will produce a final column that ___________________.

An argument is valid at the level of the Logic of Statements if the conditional formed by the conjunction of its premises as the antecedent and the conclusion as its consequent is a tautology.

Consider this argument: "If we bought the movie tickets online or asked for the student discount, we saved a dollar per ticket. We did save a dollar per ticket. So we must have bought the tickets online or asked for the student discount." Using a truth table to evaluate that argument for validity will produce a final column that ___________________.

A tautology is a grammatically correct expression that turns out to be true under every possible assignment of truth values to its component simple statements.

Construct the truth table that defines negation.

What is a simple declarative statement?

Statements A and B are __________________ in the Logic of Statements if, and only if, the bi-conditional (A ≡ B) is a tautology.

Consider this argument: "If we bought the movie tickets online, we saved a dollar per ticket. We did buy the tickets online. So we must have saved a dollar per ticket." Using a truth table to evaluate that argument for validity will produce a final column that ___________________.

________________ language is much richer than the notational language of the Logic of Declarative Statements. We can express only a limited range of the logical power of natural language using the tilde, ampersand, wedge, arrow, and triple bar.

Which of the following is the best translation of "If Lauren does not borrow my car, then she does not make it back to the campus on time for her Chemistry final and moreover she does not pass Chemistry."

Accurately and elegantly translate (~s → (~p & (~r & ~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."

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)=(q\&p)) T T T T T T F F F T F T F F T F F F F T

Which of the following is the best translation of "Lauren borrowed my car, although she could have taken her own."

Compose a conjunction 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.

According to the following truth table, how should the formula ((p & q) $\rightarrow$ ~q) be characterized? p q (p\&q) -q (p\&q)\rightarrow-q) T T T F F T F F T T F T F F T F F F T T

Which of the following correctly describes a simple statement? "A grammatically correct construction in a given language used to assert ______________.

Which of the following correctly describes a conditional statement? "A grammatically correct construction in a given language used to assert ______________.

Construct the truth table that defines the conditional.