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