Double Implication
1. p <=> q = (p => q) and (q => p)Solution:To prove `p<=>q=(p=>q)^^(q=>p)`, we have to first prepare the following truth table
| `(1)` | `(2)` | `(3)=(1)<=>(2)` | `(4)=(1)=>(2)` | `(5)=(2)=>(1)` | `(6)=(4)^^(5)` |
| `p` | `q` | `p<=>q` | `p=>q` | `q=>p` | `(p=>q)^^(q=>p)` |
| T | T | T | T | T | T |
| T | F | F | F | T | F |
| F | T | F | T | F | F |
| F | F | T | T | T | T |
from this table, we can say that columns (3) and (6) are identical.
`:. p<=>q=(p=>q)^^(q=>p)`
This material is intended as a summary. Use your textbook for detail explanation.
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