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Contradiction

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

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Contradiction

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  1. Contradiction A statement is a contradiction iff it cannot be T.

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

  3. 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

  4. Contradiction P P & -P TF F FF T * 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

  5. 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

  6. 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.

  7. 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.

  8. 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.

  9. Contradiction A -A TF TF TF TF -A is a contradiction iff A is a logical truth.

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

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

  12. Contradiction P -(P>P) TFT FFT * P -(P v -P) TF T F FF T T * 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) GOAL

  13. Contradiction 1) -P&P PA ?&-? -(-P&P) 1-? -I P -(P>P) TFT FFT * P -(P v -P) TF T F FF T T * 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.

  14. Contradiction 1) -P&P PA 2) P 1 &O 3) -P 1 &O 4) P&-P 2,3 &I 5) -(-P&P) 1-4 -I P -(P>P) TFT FFT * P -(P v -P) TF T F FF T T * 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.

  15. Contradiction P -(P>P) TFT FFT * P -(P v -P) TF T F FF T T * 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.

  16. Contradiction P -(P>P) TFT FFT * P -(P v -P) TF T F FF T T * 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. Here is a tree that shows that -P&P is a contradiction. -P&P -P P *

  17. 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

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