Exam 8: Propositional Logic I

Let B symbolize the statement "All birds are beautiful." Then ~B must symbolize all of the following, except:

"p ? q is logically equivalent to $~p\vee q$ ." This statement is:

The principle of excluded middle asserts that no statement can be both true and false at the same time.

Matching: -Any statement is a ________ instance of its own statement form.

"I will either kill you, or I will love you." This statement might be symbolized as:

The only way for a disjunction to be false is if both of the disjuncts are proven to be ________ simultaneously.

The following two arguments share the same argument form: "If wishes were horses, beggars could ride; beggars cannot ride; so wishes are not horses." "If price fixing becomes a common practice, the consumer will lose choices and taxpayers will be burdened with debt.We do not want consumers to lose choices and be burdened with debt, so we know that we should not allow price fixing."

Another term for material equivalence is material implication.

What is the symbolic representation of modus tollens?

"If you can't use a computer, you won't get a job.I can use a computer very well, so I'm going to get a good job!" What is the best symbolic representation of this argument?

~(p · ~q) is the same as:

Matching: -p ? q is ________ equivalent to ~pV q.

If an argument form is expressed as a conditional (with the conclusion as the consequent and a conjunction of the premises as the antecedent), and it shows one row on its truth table where Ts appear under the premises but an F appears under the conclusion, it may still be valid

q and ~~q mean the same thing.What does this illustrate?

A truth table for an argument contains one row in which there are Ts under the premises and an F under the conclusion.This single row shows that the entire argu- ment is invalid.

Let B mean "the bread rises" and Y abbreviate "the yeast is good." The he compound statement B ? Y correctly represents any of the following propositions, except:

"If dogs can fly, then the Earth is a sponge." Is this statement true? Why or why not?

Matching: -A conjunction is true only when both of its conjuncts are ________

How could you symbolize the statement, "I will love you unless you kiss me"?

Matching: -Two statements are logically equivalent if their biconditional is a ________.