Question

For ~(W • ~X) / ~(X • ~W) // X v W, what is the valid conclusion?

A) W ⊃ ~X
B) X v W
C) ~X v W
D) W • ~X

Answer 1

Step-by-step explanation:

To determine the valid conclusion of the given logical expression ~(W • ~X) / ~(X • ~W) // X v W, we need to simplify the expression step by step.

1. Distribute the negation symbol (~) to both terms inside the parentheses:

~(W • ~X) becomes ~W v X

~(X • ~W) becomes ~X v W

The expression now becomes ~W v X / ~X v W // X v W.

2. Applying the rule of disjunction (v), we can combine the first two terms:

~W v X / ~X v W becomes ~W v X v ~X v W.

3. Applying the rule of negation (¬), we know that ~X v X is always true, so we can simplify the expression:

~W v X v ~X v W becomes ~W v W.

4. Applying the rule of disjunction (v), we know that ~W v W is always true, regardless of the value of W:

~W v W is equivalent to T (true).

Therefore, the valid conclusion from the given logical expression is:

B) X v W

Please note that the other answer choices (A, C, and D) are not valid conclusions based on the given expression.

Answer 2

The valid conclusion for the given logical argument using disjunctive syllogism is X v W (option B). It is arrived at by understanding that if one part of the disjunction is false, the other must be true to satisfy the conclusion.

Step-by-step explanation:

The question involves understanding the logical inference rules, specifically the disjunctive syllogism.

The argument given is ~(W • ~X) / ~(X • ~W) // X v W. Following the rules of disjunctive syllogism, if W were false, then because the conclusion must be true, X would have to be true. Conversely, if X were false, W must be true; therefore, the valid conclusion from the disjunction X v W is simply X v W, which corresponds to choice B) X v W.