Contingent

A statement is contingent iff

it is neither a logical truth nor a contradiction.

Contingent

A statement is contingent iff

it is neither a logical truth nor a contradiction.

So the output row for a contingent statement must containat least one F

andat least one T.

Contingent

A statement is contingent iff

it is neither a logical truth nor a contradiction.

So the output row for a contingent statement must containat least one F

andat least one T.

Sample contingent statement: P>Q

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

ContingentTo 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.

ContingentTo 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 testfor invalidity.

ContingentTo 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 andthe tree for A is open.

ContingentTo 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 andthe tree for A is open.

Common Mistake:The tree has one open andone closed branch.

ContingentTo 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 andthe tree for A is open.

Common Mistake:The tree has one open andone closed branch.

WRONG! You need to do TWO trees.

ContingentTo 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 andthe tree for A is open.

A is not a logical truth andA is not a contradiction.

ContingentTo 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 andthe tree for A is open.

A is not a logical truth andA is not a contradiction.

ContingentTo 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 andthe tree for A is open.

A is not a logical truth andA is not a contradiction.

ContingentTo 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 andthe tree for A is open.

Sample: Here are trees that show that P>Q is contingent.

-(P>Q)P

-Q

P>Q

-P Qopen open

ContingentTo 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 andthe tree for A is open.

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