Final answer:
The student's question pertains to logic and involves the use of logical forms such as disjunctive syllogism, modus ponens, and modus tollens to deduce conclusions from given premises.
Step-by-step explanation:
Understanding Argument Forms and Validity in Logic
The student's question involves logical formulations and understanding the structure of valid arguments. It includes analyzing premises and conclusions, and utilizing logical tools like disjunctive syllogism, modus ponens, and modus tollens. Each of these logical tools represents a different form of deduction. For example, modus ponens and modus tollens reflect the understanding of necessary and sufficient conditions within conditional statements. The premises provided make use of these logical forms and are used to deduce conclusions that must follow if the premises are true.
Disjunctive syllogism allows for a conclusion to be drawn when one of a disjunction is proven false, making the other outcome inevitable. In set logic, this would be similar to saying if we have F or H, and F is not true, then H must be the case. The equivalence presented in the form of G ≡ ∼F asserts that G is true if and only if F is not true, and vice versa.
Through the process of simplification, hypothetical syllogism, implication, and equivalence, the student has derived several conclusions. This exercise reinforces the students' understanding and application of logical reasoning and the structure of arguments to reach valid conclusions.