Prove Absorption laws
1. p and (p or q) = p
Solution:
To prove `p^^(pvvq)=p`, we have to first prepare the following truth table
| `(1)` | `(2)` | `(3)=(1)vv(2)` | `(4)=(1)^^(3)` |
| `p` | `q` | `pvvq` | `p^^(pvvq)` |
| T | T | T | T |
| T | F | T | T |
| F | T | T | F |
| F | F | F | F |
from this table, we can say that columns (4) and (1) are identical.
`:. p^^(pvvq)=p`
2. p or (p and q) = p
Solution:
To prove `pvv(p^^q)=p`, we have to first prepare the following truth table
| `(1)` | `(2)` | `(3)=(1)^^(2)` | `(4)=(1)vv(3)` |
| `p` | `q` | `p^^q` | `pvv(p^^q)` |
| T | T | T | T |
| T | F | F | T |
| F | T | F | F |
| F | F | F | F |
from this table, we can say that columns (4) and (1) are identical.
`:. pvv(p^^q)=p`
This material is intended as a summary. Use your textbook for detail explanation.
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