Question

For A ⊃ (N v Q) / ~(N v ~A) // A ⊃ Q, what is the valid conclusion?

A) A ⊃ N
B) ~(N v ~A)
C) A ⊃ Q
D) N v Q

Answer 1

Step-by-step explanation:

To determine the valid conclusion from the given logical expression A ⊃ (N v Q) / ~(N v ~A) // A ⊃ Q, let's simplify and analyze the expression.

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

A ⊃ (N v Q) / ~(N v ~A) // A ⊃ Q

A ⊃ (N v Q) / ~(N v ~A) and A ⊃ Q [Ignoring the double forward slash "//" since it does not affect the inference]

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

From the first part, A ⊃ (N v Q), we cannot directly infer any of the given options.

From the second part, ~(N v ~A), we cannot directly infer any of the given options.

However, combining the first part (A ⊃ (N v Q)) and the third part (A ⊃ Q), we can infer A ⊃ (N v Q) AND (A ⊃ Q).

Simplifying further, we can rewrite A ⊃ (N v Q) AND (A ⊃ Q) as A ⊃ (N v Q) • (~A v Q).

From this expression, we can infer:

A) A ⊃ N, since ~A is part of the expression.

C) A ⊃ Q, since Q is part of the expression.

However, we cannot directly infer:

B) ~(N v ~A), since the expression does not provide enough information to determine the relationship between N and A.

D) N v Q, since N and Q are already part of the given expression.

Therefore, the valid conclusions are:

A) A ⊃ N

C) A ⊃ Q

Answer 2

The valid conclusion is A ⊃ Q.

Step-by-step explanation:

The valid conclusion is A ⊃ Q.

To reach this conclusion, we need to use the premise A ⊃ (N v Q) and the additional premise ~(N v ~A).

By assuming the negation of our desired conclusion ~(A ⊃ Q), we can derive a contradiction, which allows us to conclude that the assumption is false. This in turn establishes the validity of the conclusion A ⊃ Q.