Question

Some of the arguments are valid, whereas others exhibit the converse or the inverse error. Use symbols to write the logical form of each argument. If the argument is valid, identify the rule of inference that guarantees its validity. Otherwise, state whether the converse or the inverse error is made. If this computer program is correct, then it produces the correct output when run with the test data my teacher gave me. This computer program produces the correct output when run with the test data my teacher gave me.

∴

This computer program is correct.

Let p = "this computer program is correct," and let q = "this computer program produces the correct output when run with the test data my teacher gave me." Is the argument valid or invalid? Select the answer that shows the symbolic form of the argument and justifies your conclusion.

Answer 1

Hi, you've asked an incomplete/unclear question. I inferred you want a symbolic representation and validity of the argument mentioned.

Answer:

argument is valid

Step-by-step explanation:

Let's break down the arguments into parts:

Let,

p = "if this computer program is correct,"

q = "this computer program produces the correct output when run with the test data my teacher gave me."

c = "This computer program is correct."

Meaning, p ⇒ q (p results in q), then we can conclude that,

(p ⇒ q ) ∴ ⇒ c

However, the correct converse of the statement is:

If this computer program produces the correct output when run with the test data my teacher gave me, then the computer program is correct,"

q ⇒ p (If q then p)

While the correct inverse of the statement is:

If this computer program is not correct, then this computer program does not produce the correct output when run with the test data my teacher gave me."