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

2. 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.

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 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 *

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

10. 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

11. 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 *

12. 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

13. 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

14. 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

15. 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 *

16. 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 *

17. 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