Laws for Contradiction
1. p or c = p
Solution:
To prove `pvvc=p`, we have to first prepare the following truth table
| `(1)` | `(2)` | `(3)=(1)vv(2)` |
| `p` | `c` | `pvvc` |
| T | F | T |
| F | F | F |
from this table, we can say that columns (3) and (1) are identical.
`:. pvvc=p`
2. p and c = c
Solution:
To prove `p^^c=c`, we have to first prepare the following truth table
| `(1)` | `(2)` | `(3)=(1)^^(2)` |
| `p` | `c` | `p^^c` |
| T | F | F |
| F | F | F |
from this table, we can say that columns (3) and (2) are identical.
`:. p^^c=c`
3. p or not p = c
Solution:
To prove `pvv~p=c`, we have to first prepare the following truth table
| `(1)` | `(2)` | `(3)=~(1)` | `(4)=(1)vv(3)` |
| `p` | `c` | `~p` | `pvv~p` |
| T | F | F | T |
| F | F | T | T |
from this table, we can say that columns (4) and (2) are not identical.
`:. pvv~p!=c`
This material is intended as a summary. Use your textbook for detail explanation.
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