contradiction
DESCRIPTION
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 . - PowerPoint PPT PresentationTRANSCRIPT
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 Fson the output column.
Contradiction
A statement is a contradiction iff
it cannot be T.
So its truth table has all Fson 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 Fson the output column.
Sample: A Standard Contradiction: P&-P
P P & -PT F FF F T *
Contradiction
A statement is a contradiction iff
it cannot be T.
So its truth table has all Fson 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 Fson 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 Fson 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 Fson 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 -AT FT FT FT F
Contradiction
-A is a contradiction iff
A is a logical truth.
So these must be contradictions: -(P>P) -(Pv-P) P<>-P
A -AT FT FT FT F
ContradictionTo show a statement A is a contradiction ... with a table: The output row for A has all Fs.
P -(P>P)T F TF F T *
P -(P v -P)T F T FF F T T *
ContradictionTo 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 TF F T *
P -(P v -P)T F T FF F T T *
-(-P&P) GOAL
ContradictionTo 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 TF F T *
P -(P v -P)T F T FF F T T *
1) -P&P PA
?&-? -(-P&P) 1-? -I
ContradictionTo 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 TF F T *
P -(P v -P)T F T FF F T T *
1) -P&P PA2) P 1 &O3) -P 1 &O4) P&-P 2,3 &I5) -(-P&P) 1-4 -I
ContradictionTo 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 TF F T *
P -(P v -P)T F T FF F T T *
ContradictionTo 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 TF F T *
P -(P v -P)T F T FF F T T *
Here is a tree that shows that -P&P is a contradiction.-P&P
-PP*
ContradictionTo 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.
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