1. Generate the truth table for Expression : p and (q or r)=(p and q) or (p and r)Solution:To prove `p^^(qvvr)=(p^^q)vv(p^^r)`, we havet to first prepare the following truth table
| `(1)` | `(2)` | `(3)` | `(4)=(2)vv(3)` | `(5)=(1)^^(4)` | `(6)=(1)^^(2)` | `(7)=(1)^^(3)` | `(8)=(6)vv(7)` |
| `p` | `q` | `r` | `qvvr` | `p^^(qvvr)` | `p^^q` | `p^^r` | `(p^^q)vv(p^^r)` |
| T | T | T | T `T=TvvT` | T `T=T^^T` | T `T=T^^T` | T `T=T^^T` | T `T=TvvT` |
| T | T | F | T `T=TvvF` | T `T=T^^T` | T `T=T^^T` | F `F=T^^F` | T `T=TvvF` |
| T | F | T | T `T=FvvT` | T `T=T^^T` | F `F=T^^F` | T `T=T^^T` | T `T=FvvT` |
| T | F | F | F `F=FvvF` | F `F=T^^F` | F `F=T^^F` | F `F=T^^F` | F `F=FvvF` |
| F | T | T | T `T=TvvT` | F `F=F^^T` | F `F=F^^T` | F `F=F^^T` | F `F=FvvF` |
| F | T | F | T `T=TvvF` | F `F=F^^T` | F `F=F^^T` | F `F=F^^F` | F `F=FvvF` |
| F | F | T | T `T=FvvT` | F `F=F^^T` | F `F=F^^F` | F `F=F^^T` | F `F=FvvF` |
| F | F | F | F `F=FvvF` | F `F=F^^F` | F `F=F^^F` | F `F=F^^F` | F `F=FvvF` |
from this table, we can say that columns (5) and (8) are identical.
`:. p^^(qvvr)=(p^^q)vv(p^^r)`
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