Given the statements: R ⊃ M / C ⊃ E / M ⊃ ∼ E / R • C
These statements are:
A) Contradictory.
B) Tautologous.
C) Valid.
D) Inconsistent.
E) Consistent.

Question

Quizplus · Accepted Answer

We can use the method of proof by contradiction to show that these statements are inconsistent. Assume that they are consistent. Then, we can use the premises and the rule of inference of modus ponens to derive the following:
1. R ⊃ M (premise)
2. M ⊃ ∼ E (premise)
3. C ⊃ E (premise)
4. R (premise)
5. M (modus ponens with 1 and 4)
6. ∼ E (modus ponens with 2 and 5)
7. E (modus ponens with 3 and 4)
8. E • ∼ E (conjunction of 6 and 7)
Step 8 is a contradiction, since a conjunction of a statement and its negation is always false. Therefore, our assumption that the statements are consistent must be false, and they are inconsistent.

Given the Statements: R ⊃ M / C ⊃ E