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Understanding Contingent Statements with Tables and Trees

Learn about contingent statements and how to identify them using truth tables and proof trees. Contingent statements are neither logical truths nor contradictions and require at least one true and one false output. No proof test is possible for contingent statements, and common mistakes to avoid are highlighted.

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Understanding Contingent Statements with Tables and Trees

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  1. Contingent A statement is contingent iff it is neither a logical truth nor a contradiction.

  2. Contingent A statement is contingent iff it is neither a logical truth nor a contradiction. So the output row for a contingent statement must contain at least one F and at least one T.

  3. Contingent A statement is contingent iff it is neither a logical truth nor a contradiction. So the output row for a contingent statement must contain at least one F and at least one T. Sample contingent statement: P>Q

  4. Contingent To show a statement A is contingent ... with a table: The output row for A has a F and a T.

  5. Contingent To show a statement A is contingent ... with a table: The output row for A has a F and a T. with a proof: No proof test is possible.

  6. Contingent To show a statement A is contingent ... with a table: The output row for A has a F and a T. with a proof: No proof test is possible. There is also no proof test for invalidity.

  7. Contingent To show a statement A is contingent ... with a table: The output row for A has a F and a T. with a proof: No proof test is possible. with a tree: The tree for -A is open and the tree for A is open.

  8. Contingent To show a statement A is contingent ... with a table: The output row for A has a F and a T. with a proof: No proof test is possible. with a tree: The tree for -A is open and the tree for A is open. Common Mistake: The tree has one open and one closed branch.

  9. Contingent To show a statement A is contingent ... with a table: The output row for A has a F and a T. with a proof: No proof test is possible. with a tree: The tree for -A is open and the tree for A is open. Common Mistake: The tree has one open and one closed branch. WRONG! You need to do TWO trees.

  10. Contingent To show a statement A is contingent ... with a table: The output row for A has a F and a T. with a proof: No proof test is possible. with a tree: The tree for -A is open and the tree for A is open. A is not a logical truth and A is not a contradiction.

  11. Contingent To show a statement A is contingent ... with a table: The output row for A has a F and a T. with a proof: No proof test is possible. with a tree: The tree for -A is open and the tree for A is open. A is not a logical truth and A is not a contradiction.

  12. Contingent To show a statement A is contingent ... with a table: The output row for A has a F and a T. with a proof: No proof test is possible. with a tree: The tree for -A is open and the tree for A is open. A is not a logical truth and A is not a contradiction.

  13. Contingent To show a statement A is contingent ... with a table: The output row for A has a F and a T. with a proof: No proof test is possible. with a tree: The tree for -A is open and the tree for A is open. Sample: Here are trees that show that P>Q is contingent. -(P>Q) P -Q P>Q -P Q open open

  14. Contingent To show a statement A is contingent ... with a table: The output row for A has a F and a T. with a proof: No proof test is possible. with a tree: The tree for -A is open and the tree for A is open. For more click here

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