Contradiction A statement is a contradiction iff it

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 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 T F P & -P 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 T T -A F F

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

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

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

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

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

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

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