A given sentential formula is a tautology if and only if: Its negation has all t

Question

A given sentential formula is a tautology if and only if: Its negation has all tree-paths closed. It has all tree paths closed. It does not have all tree paths closed. A given sentential formula is a contradiction if and only if: Its negation has all tree-paths closed. It has all tree paths closed. It does not have all tree paths closed. Use the tree method to determine if the following set of sentences is consistent. CONSISTENT/INCONSISTENT Use the tree method to determine if the following sentence is a tautology. ((p superset q) superset p) superset p TAUTOLOGY- Not a Tautology Use the tree method to determine if the following argument form are valid or invalid. p superset q tilde p superset q/-q VALID-INVALID p v q p superset r q superset r/- r VALID-INVALID p superset q p superset r/- q superset r VALID-INVALID p congruent tilde q/- p congruent q VALID-INVALID

Explanation / Answer

3)

Tautology: to test whether a formula is a tautology, negate the formula and check to see if the negation is a contradiction. If the negation of the formula is a contradiction, then the original formula is a tautology. However, if there is at least one path that is open, then the negation of the formula is consistent, and so the original formula is not a tautology.

option A

4)

To test a sentence for being a contradiction, make the sentence the first line
of a truth tree. If there is an open path in the tree, this path provides a
counterexample to the sentence being a contradiction. If all paths close, the
sentence is a contradiction.

option:B

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