A statement is a contradiction iff it cannot be T.

A statement is a contradiction So its truth table has all Fs iff it cannot be T. So its truth table has all Fs on the output column.

Contradiction A statement is a contradiction iff it cannot be T. So its truth table has all Fs on the output column. Sample: A Standard Contradiction: P&-P

Contradiction A statement is a contradiction iff it cannot be T. So its truth table has all Fs on the output column. Sample: A Standard Contradiction: P&-P P P & -P T F F F F T *

Contradiction A statement is a contradiction iff it cannot be T. So its truth table has all Fs on the output column. Sample: A Standard Contradiction: P&-P Standard Contradictions are not the only ones. -(P>P) -(Pv-P) P<>-P

Contradiction A statement is a contradiction iff it cannot be T. So its truth table has all Fs on the output column. -(P>P) -(Pv-P) P<>-P Contradictions are Bad News: They must be false.

Contradiction A statement is a contradiction iff it cannot be T. So its truth table has all Fs on the output column. -(P>P) -(Pv-P) P<>-P Contradictions are Bad News: They must be false. They carry no information.

Contradiction A statement is a contradiction iff it cannot be T. So its truth table has all Fs on the output column. -(P>P) -(Pv-P) P<>-P Contradictions are Bad News: They must be false. They carry no information. Lousy Weather Report: it is raining and not raining.

Contradiction -A is a contradiction iff A is a logical truth. A -A T F

So these must be contradictions: -(P>P) -(Pv-P) P<>-P -A is a contradiction iff A is a logical truth. So these must be contradictions: -(P>P) -(Pv-P) P<>-P A -A T F

Contradiction To show a statement A is a contradiction ... with a table: The output row for A has all Fs. P -(P>P) T F T F F T * P -(P v -P) T F T F F F T T *

Contradiction To show a statement A is a contradiction ... with a table: The output row for A has all Fs. with a proof: Prove -A. Here is a proof that -P&P is a contradiction. P -(P>P) T F T F F T * P -(P v -P) T F T F F F T T * -(-P&P) GOAL

Contradiction To show a statement A is a contradiction ... with a table: The output row for A has all Fs. with a proof: Prove -A. Here is a proof that -P&P is a contradiction. P -(P>P) T F T F F T * P -(P v -P) T F T F F F T T * 1) -P&P PA ?&-? -(-P&P) 1-? -I

Contradiction To show a statement A is a contradiction ... with a table: The output row for A has all Fs. with a proof: Prove -A. Here is a proof that -P&P is a contradiction. P -(P>P) T F T F F T * P -(P v -P) T F T F F F T T * 1) -P&P PA 2) P 1 &O 3) -P 1 &O 4) P&-P 2,3 &I 5) -(-P&P) 1-4 -I

Contradiction To show a statement A is a contradiction ... with a table: The output row for A has all Fs. with a proof: Prove -A. with a tree: The tree for A closes. P -(P>P) T F T F F T * P -(P v -P) T F T F F F T T *

Here is a tree that shows that -P&P is a contradiction. To show a statement A is a contradiction ... with a table: The output row for A has all Fs. with a proof: Prove -A. with a tree: The tree for A closes. P -(P>P) T F T F F T * P -(P v -P) T F T F F F T T * Here is a tree that shows that -P&P is a contradiction. -P&P -P P *

For more click here Contradiction To show a statement A is a contradiction ... with a table: The output row for A has all Fs. with a proof: Prove -A. with a tree: The tree for A closes. For more click here