A common misconception. It may seem plausible that we can tell whether a sentence is a tautology—i.e., true on every interpretation—by starting a tree with the sentence itself— undenied—and finding that when the tree is completed, all the branches are open. Try this method on a. and b. and show that it gives the wrong answers; then address c.

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A common misconception. It may seem plausible that we can tell whether a sentence is a tautology—i.e., true on every interpretation—by starting a tree with the sentence itself— undenied—and finding that when the tree is completed, all the branches are open. Try this method on a. and b. and show that it gives the wrong answers; then address c.

17. A common misconception. It may seem plausible that we can tell whether a sentence is a tautology—i.e., true on every interpretation—by starting a tree with the sentence itself— undenied—and finding that when the tree is completed, all the branches are open. Try this method on a. and b. and show that it gives the wrong answers; then address c.

a. A

b. (A v ~A) v (A & ~A)

c. QUESTION. Does this bogus test always give wrong answers?

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