Exam 9: Propositional Logic II

Which is not one of the nine rules of inference?

Matching: -If no truth values can be given to the statements of an argument to make its premises true and its conclusion false, then the argument must be ________.

Which of the rules of inference is described by this formula? (p ? q) · (r ? s) $p\vee r$ ? $q\vee s$

What is the formula for simplification?

Conjunction is symbolically represented by p, q, ? p · q.

Matching: -We can use ________ to substitute (p ? q) for (~pV q)

One of De Morgan's theorems states that $(p\vee q)$ is logically equivalent to $(q\vee p)$ .

Matching: -When the rule of ________ is applied to "If it rains, I will get wet," it becomes "If it rains, not only will it be raining but I will get wet."

Which rule of inference makes the conclusion of this argument follow from its premise? A ? B ? (~A ? ~B)

Matching: -"p · q, ? p" is the form of ________.

The method of proving invalidity by assigning truth values to statements in a shortened truth table:

You can replace [(p · q) ?r] with [p ?(q ?r)].

What is the rule of inference by which the conclusion of this argument follows from the premise? C ? (A ? B) ? C ? (~~A ? B)

Which rule of inference makes the conclusion of this argument follow from its premise? $[F ? ~(G \vee H)] ? (I \vee J) ?{[F ? ~(G\vee H)] · [F ? ~(G \vee H)]} ? (I \vee J)$

Simplification is symbolically represented by p ? q, ? (p · q).

By which rule of inference does the conclusion of this argument follow from its premises? $~(A · B)$ ? $(C \vee D)$ ~ $(A · B)$ ? $(C \vee D)$

For the following valid argument, state the rule of inference by which the conclusion follows from its premises: $[F ? (G ? ~H)] \vee(I \vee J) ~[F ? (G ? ~H)]$ ? $I \vee J$

Material implication states that $(~p\vee q)$ is logically equivalent to (p ?q).

Matching: -An argument is proved invalid when its premises are ________ and its conclusion is false in one line of its truth table.

"Either I get married or I live alone; I didn't get married; therefore, I live by myself." What is the elementary valid argument form of this argument?