Question

Use symbols to write the logical form of each of the following arguments. Then state whether or not the argument is valid. If it is valid, state which of the following rules of inference apply (Modus Ponens - Method of Affirming, Modus Tollens - Method of Denying, Generalization, Specialization, Elimination, Transitivity, or Division by Cases). If the argument is not valid, state whether the Inverse error or Converse error was made.

a) if n is an integer, then n is a rational number

n is a rational number

Therefore, n is an integer

b) x is a positive or x is negative

if x is positive, then x^2 >0

if x is negative then x^2>0

therefore, x^2 >0

c)if ABCD is a square, then it is a rhombus

ABCD is not a rhombus

Therefore, ABCD is not a square

Answer 1

Part-A:

.

If n is an integer then n is obviously a rational number (Method of Affirming)

Also it is a generalization of the fact that every integer is a rational number (Generalization).

Note that the converse is an error because we know

but it is definitely not an integer.

Part-B:

The argument is valid.

Note that if

The converse is true for any

Either or is always positive.

Part-C:

is a square is a rhombus.

It may be termed as generalization.

But the converse is not true.

Since a square has an angle of between its sides but a rhombus does not,so a rhombus is not a square.