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