Some of the arguments are valid by universal modus ponens or universal modus tol

Question

Some of the arguments are valid by universal modus ponens or universal modus tollens; others are invalid and exhibit the converse or the inverse error. State which are valid and which are invalid. Justify your answers by showing all work and steps required.

Any sum of two rational numbers is rational.
The sum r + s is rational.                                                                                                                                                                     The numbers r and s are both rational.

Is the solution suppose to be universal modus ponens or is it by converse error?

Explanation / Answer

Let p : r and s are both rational q: The sum of r and s is rational

The given statements become

x y (p(x,y) -> q(x,y))

q(x,y)

---------------------------

p(x,y)

This is not universal modus ponens. Universal modus ponens is

x y (q(x,y) -> p(x,y))

q(x,y)

---------------------------------

p(x,y)

x y (q(x,y) -> p(x,y)) which is the converse of x y (p(x,y) -> q(x,y)) is not the same as it. Thus this is the converse error.

Related Questions

Navigate

• Browse (All)
• Browse S
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.