Question

Given the following premises:

1. D⊃(∼A∨∼A)
2. ∼A⊃(R∙M)
3. ∼R∙∼M
a. D⊃∼A1, Taut
b. D⊃A1,DN
c. D⊃(R∙M)1,2,HS
d. ∼∼A2,3,MT
e. ∼(R∙M) 3, DM

Answer 1

The question involves applying logical reasoning forms such as disjunctive syllogism, modus ponens, and modus tollens, to structure the premises given and deduce valid conclusions in a deductive argument.

Step-by-step explanation:

The student's question involves understanding logical argument patterns and how to apply different forms of logical reasoning such as disjunctive syllogism, modus ponens, and modus tollens. These forms of argument are central to deductive reasoning, where the validity of an argument is determined by its form rather than the actual truth of the premises. In disjunctive syllogism, the argument takes the form:

1. X or Y.
2. Not Y.
3. Therefore X.

For modus ponens, the pattern is:

1. P → Q (If P then Q)
2. P is true.
3. Therefore, Q must be true.

And in the case of modus tollens:

1. P → Q (If P then Q)
2. Q is not true.
3. Therefore, P cannot be true.

By understanding these logical forms and applying them to the student's premises, one can deduce valid conclusions based on the structure of the argument.