Final answer:
The proposition that is neither a tautology nor a contradiction from the given options is – (p∧q) ⟶ q, as it can be true or false depending on the truth values of 'p' and 'q'.
Step-by-step explanation:
The student is asking to identify the proposition that is neither a tautology nor a contradiction among the provided statements. A tautology is a statement that is always true, and a contradiction is a statement that is always false. To determine which proposition fits this criterion, we need to analyze each proposition.
–(p∧q) ⟶ q: This is a conditional statement that is true whenever 'p AND q' is true or when 'q' is true on its own. It is not a tautology as there are instances where the statement can be false (e.g., when 'p' is true and 'q' is false), nor is it a contradiction since it can be true.
– (p∨q)⟶q: This statement is also a conditional, but it leans more towards being a tautology because if 'q' is true, the whole statement is true and if 'p' is true or 'q' is true, the statement is still true.
– q⟶(p∨q): This is a tautology since whenever 'q' is true, '(p OR q)' is inevitably true as well.
– (p∧¬p)⟶q: This is a contradiction. 'p AND NOT p' cannot ever be true, making the antecedent always false, thus this statement is always true by the definition of a material conditional in logic, which states that a conditional is true if the antecedent is false.
The proposition that is neither a tautology nor a contradiction is (p∧q) ⟶ q because it can be either true or false depending on the truth values of 'p' and 'q'.