Question

Given C ≣ D / E v ~D // E⊃C, what follows?
A) D ⊃ C
B) E ⊃ C
C) ~D v E
D) C

Answer 1

Step-by-step explanation:

To determine what follows from the given logical expression C ≣ D / E v ~D // E⊃C, let's simplify and analyze the expression.

1. Let's simplify the expression step by step:

C ≣ D / E v ~D // E⊃C

(C ≡ D) / (E v ~D) // E⊃C [Using the material implication A ⊃ B ≡ ~A v B]

2. Now, let's analyze the simplified expression:

From the first part, C ≡ D, we cannot directly infer any of the given options.

From the second part, E v ~D, we cannot directly infer any of the given options.

However, combining the first part (C ≡ D) and the third part (E⊃C), we can infer C ≡ D AND (E⊃C).

Simplifying further, we can rewrite C ≡ D AND (E⊃C) as (C ≡ D) • (~E v C).

From this expression, we can infer:

B) E ⊃ C, since ~E is part of the expression.

Additionally, we can also infer:

C) ~D v E, since E is part of the expression.

However, we cannot directly infer:

A) D ⊃ C, since the expression does not provide enough information to determine the relationship between D and C.

D) C, since C is already part of the given expression.

Therefore, the correct inferences are:

B) E ⊃ C

C) ~D v E

Answer 2

The given expression C ≣ D / E v ~D // E⊃C can be simplified to (~D ⊃ E) ⊃ C. So the answer is A) D ⊃ C.

Step-by-step explanation:

The given expression C ≣ D / E v ~D // E⊃C can be simplified using logical equivalences. Let's break it down step by step:

1. C ≣ D / E v ~D // E⊃C can be rewritten as (D / E v ~D) // E⊃C using the associativity of // (biconditional) operator.

2. (D / E v ~D) // E⊃C can be further simplified as (D / E v ~D) ⊃ E⊃C using the transitivity of // operator.

3. (D / E v ~D) ⊃ E⊃C can be simplified as (~D ⊃ E) ⊃ C using the transitivity of // operator.

Therefore, the resulting expression is (~D ⊃ E) ⊃ C. So the answer is A) D ⊃ C.