Question

If A⊃B / (A • B) ⊃ C / A ⊃ (C⊃D) // A⊃D, what follows?

A) B ⊃ C
B) A ⊃ D
C) C ⊃ D
D) A • B

Answer 1

herefore, option B) A ⊃ D follows.

Step-by-step explanation:

To solve the given problem, we will use the rules of propositional logic. The proof can be done using a process called "conditional proof."

1. A⊃B / (A • B) ⊃ C / A ⊃ (C⊃D) // A⊃D (Given)

2. A⊃B (Premise)

3. (A • B) ⊃ C (Premise)

4. A (Assumption for Conditional Proof)

5. B (Modus Ponens, 2, 4)

6. A • B (Conjunction, 4, 5)

7. C (Modus Ponens, 3, 6)

8. C⊃D (Premise)

9. D (Modus Ponens, 7, 8)

10. A ⊃ D (Conditional Proof, 4-9)

From the given premises and using conditional proof, we are able to derive A⊃D. Therefore, option B) A ⊃ D follows.

Answer 2

To prove that A⊃D follows from the given premises, we can use the Law of Syllogism. The Law of Syllogism states that if a conditional statement is true and its consequent implies another statement, then the antecedent of the second statement is also true.

Step-by-step explanation:

To prove that A⊃D follows from the given premises, we can use the Law of Syllogism. The Law of Syllogism states that if a conditional statement is true and its consequent implies another statement, then the antecedent of the second statement is also true.

In this case, we have:

1. A⊃B (given premise)

2. (A • B) ⊃ C (given premise)

3. A ⊃ (C⊃D) (given premise)

From premise 1 and premise 3, we can conclude that A⊃(C⊃D) is true.

From premise 2 and the derived conclusion, we can use the Law of Syllogism again to conclude that A⊃D is true.

Therefore, the correct answer is option B) A ⊃ D.