A contradiction is a statement that is false under every possible assignment of truth values to its variables. The expression P ∧ ¬P asserts that P is both true and not true at the same time, which cannot occur. In any valuation, either P is true or P is false; in neither case can the conjunction of P and its negation be true. Hence this expression is always false and is a standard example of contradiction.
Option A:
Option A directly combines a proposition with its own negation using “and,” ensuring that no scenario makes the whole statement true.
Option B:
Option B, P ∨ ¬P, is actually a tautology, as it is always true regardless of P’s value.
Option C:
Option C can be true or false depending on the values of P and Q, so it is a contingency, not a permanent contradiction.
Option D:
Option D, P → Q, is also contingent; its truth depends on how P and Q are valued.
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