Question

Prove that the following argument forms are valid using the natural deduction method. You can use any of the rules that we have covered listed below the problem.

a. Modus Ponens
b. Modus Tollens
c. Disjunctive Syllogism
d. Hypothetical Syllogism

Answer 1

To prove the validity of the argument forms using the natural deduction method, we can use the rules of Modus Ponens, Modus Tollens, Disjunctive Syllogism, and Hypothetical Syllogism.

Step-by-step explanation:

To prove the validity of the argument forms using the natural deduction method, we can use the rules of Modus Ponens, Modus Tollens, Disjunctive Syllogism, and Hypothetical Syllogism.

a. Modus Ponens:

1. If X is true, then Y is true.
2. X is true.
3. Therefore, Y is true.

b. Modus Tollens:

1. If X is true, then Y is true.
2. Y is not true.
3. Therefore, X is not true.

c. Disjunctive Syllogism:

1. X or Y is true.
2. Not Y is true.
3. Therefore, X is true.

d. Hypothetical Syllogism:

1. If P is true, then Q is true.
2. If Q is true, then R is true.
3. Therefore, if P is true, then R is true.