Question

These arguments isF ⊃ ∼K∼N ⊃ F∼N ⊃ ∼K

a. MT-valid.
b. HS-valid.
c. Invalid.
d. DD-invalid.
e. CD-valid.

Answer 1

The question requires evaluating the validity of deductive arguments. It does not present a clear disjunctive syllogism, and additional context is required to determine the validity of the given arguments.

Step-by-step explanation:

The question involves analyzing the validity of deductive arguments. Validity in logic means that if the premises are true, then the conclusion must necessarily be true. One common valid argument structure is the disjunctive syllogism. This argument structure takes the form:

X or Y.

Not Y.

Therefore, X.

The given arguments do not form a disjunctive syllogism, hence we cannot apply this rule directly. Instead, we need to consider other rules of inference to evaluate the validity of the arguments provided. A valid deductive inference, such as modus tollens or hypothetical syllogism, could be applicable here. However, without a clear conclusion stated, determining the type of argument and its validity requires more context or additional premises.

Answer 2

In this case the argument isF ⊃ ∼K∼N ⊃ F∼N ⊃ ∼K can be classified as: HS-valid.

The answer is option ⇒b

Step-by-step explanation:

To determine the validity of the given arguments, we need to apply logical reasoning rules and analyze the structure of the statements. Let's break down the given argument:

These arguments isF ⊃ ∼K∼N ⊃ F∼N ⊃ ∼K

We can rewrite the argument with brackets to indicate the order of operations:

(1) isF ⊃ (∼K∼N) ⊃ (F∼N) ⊃ ∼K

Now let's evaluate each part of the argument using logical reasoning rules:

(1) isF ⊃ (∼K∼N)

This is a conditional statement. To determine its validity, we can apply the Material Implication (MI) rule. The MI rule states that if we have a conditional statement of the form "A ⊃ B", we can replace it with "∼A ∨ B".

Using the MI rule, we can rewrite the statement as:

∼isF ∨ (∼K∼N)

Next, let's evaluate the second part of the argument:

(∼K∼N) ⊃ (F∼N)

This is another conditional statement. We can apply the MI rule to rewrite it as:

∼(∼K∼N) ∨ (F∼N)

This can be simplified to:

K∼N ∨ (F∼N)

Finally, let's evaluate the last part of the argument:

(F∼N) ⊃ ∼K

Again, we can apply the MI rule to rewrite it as:

∼(F∼N) ∨ ∼K

This can be simplified to:

∼F ∨ ∼N ∨ ∼K

Now, let's combine all the simplified statements:

∼isF ∨ (∼K∼N) ⊃ K∼N ∨ (F∼N) ⊃ ∼F ∨ ∼N ∨ ∼K

By observing the structure of the argument, we can see that it follows the Hypothetical Syllogism (HS) rule. The HS rule states that if we have two conditional statements of the form "A ⊃ B" and "B ⊃ C", we can conclude "A ⊃ C".

Since our argument can be rewritten as:

(∼isF ∨ (∼K∼N)) ⊃ (K∼N ∨ (F∼N)) ⊃ (∼F ∨ ∼N ∨ ∼K)

We can see that the first two parts form a conditional statement, and the last part forms the consequent of the conditional statement.

Based on the analysis, the argument can be classified as: b. HS-valid.

Therefore, option b is the correct answer.