Final answer:
The propositional form P∧(P⟶Q)∧¬Q is a contradiction because it asserts that Q must both be true and false simultaneously, which is logically impossible.
Step-by-step explanation:
The student is asking whether the propositional form P∧(P⟶Q)∧¬Q is a tautology, a contradiction, or neither. To determine this, we need to examine the logical form of the expression. The symbol ∧ represents logical AND, ⟶ represents a biconditional (if and only if), and ¬ represents negation.
A tautology is a propositional form that is true under every possible valuation of its variables, whereas a contradiction is false under every valuation. An expression that is neither always true nor always false is neither a tautology nor a contradiction.
If 'P' is true, then 'P ⟶ Q' indicates that 'Q' must also be true, hence 'P ∧ (P⟶Q)' would be true only if both 'P' and 'Q' are true. However, the expression also contains '¬Q', which is the negation of 'Q' and states that 'Q' is false. Thus, 'P∧(P⟶Q)∧¬Q' contains a direct contradiction because it asserts that 'Q' is both true and false simultaneously, which is logically impossible. Therefore, the propositional form is a contradiction.