Question

Discrete Mathematics

(a) Consider the following argument:

All honest people pay their taxes.

Darth is not honest.

∴ Darth does not pay his taxes.

Write this argument in formal language using quantiﬁers, variables, and predicates (remember to deﬁne what your predicate means). Is this argument valid? If so, is it universal modus ponens or universal modus tollens? If not, does it exhibit converse error or inverse error?

(b) Draw a diagram with disks (as shown in the text) to help demonstrate whether the following argument is valid or invalid.

All polynomial functions are diﬀerentiable.

All diﬀerentiable functions are continuous.

∴ All polynomial functions are continuous.

Answer #1

Discrete Mathematics
(a) Consider the following argument:
All honest people pay their taxes.
Darth is not honest.
∴ Darth does not pay his taxes.
Write this argument in formal language using quantiﬁers,
variables, and predicates (remember to deﬁne what your predicate
means). Is this argument valid? If so, is it universal modus ponens
or universal modus tollens? If not, does it exhibit converse error
or inverse error?
(b) Draw a diagram with disks (as shown in the text) to...

Consider the argument: "Each of five roommates, Melissa, Aaron,
Ralph, Veneesha, and Keeshawn, has taken a course in discrete
mathematics. Every student who has taken a course in discrete
mathematics can take a course in algorithms. Therefore, all five
roommates can take a course in algorithms next year."
Let r(x) denote "x is one of the five
roommates listed".
Let d(x) denote "x has taken a course
in discrete mathematics".
Let a(x) denote "x can take a course
in algorithms"....

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