Question

These statements are:R ⊃ (M ∨ ∼ C) / (P ∨ U) ⊃ C / M ⊃ ∼ P / R ≡ U

a.consistent
b.Non consistent

Answer 1

The given statements R ⊃ (M ∨ ~C) and (P ∨ U) ⊃ C are nonconsistent.

Step-by-step explanation:

The given statements are R ⊃ (M ∨ ~C) and (P ∨ U) ⊃ C. We need to determine the consistency of these statements.

To do this, we will use a proof by contradiction. We will assume that the statements are consistent and then derive a contradiction.

Assumption:

Assume that the statements R ⊃ (M ∨ ~C) and (P ∨ U) ⊃ C are consistent.

Derivation:

1. Assume R is true.
2. Using the first statement, we have (M ∨ ~C) is true.
3. Case 1: Assume M is true. Then, using the second statement, (P ∨ U) ⊃ C is true.
4. But this contradicts our assumption that R is true and implies that C is false.
5. Case 2: Assume ~C is true. Then, using the first statement, R ⊃ (M ∨ ~C) implies that R is false, which contradicts our initial assumption.
6. Since both cases lead to contradictions, our assumption that the statements are consistent must be false.
7. Therefore, the statements R ⊃ (M ∨ ~C) and (P ∨ U) ⊃ C are nonconsistent.