| p |
q |
r |
~p |
~q |
~r |
~r→~p (≡~p) |
q∧(~r→~p) (≡q∧~p) |
r∨(q∧(~r→~p))
(≡r∨(q∧~p)) |
p∨~q (≡~q∨p) |
r∧(p∨~q) (≡r∧(~q∨p)) |
| 0 |
0 |
0 |
1 |
1 |
1 |
1 |
0 |
0 |
1 |
0 |
| 0 |
0 |
1 |
1 |
1 |
0 |
1 |
0 |
1 |
1 |
1 |
| 0 |
1 |
0 |
1 |
0 |
1 |
1 |
1 |
1 |
0 |
0 |
| 0 |
1 |
1 |
1 |
0 |
0 |
1 |
1 |
1 |
0 |
0 |
| 1 |
0 |
0 |
0 |
1 |
1 |
0 |
0 |
0 |
1 |
0 |
| 1 |
0 |
1 |
0 |
1 |
0 |
0 |
0 |
1 |
1 |
1 |
| 1 |
1 |
0 |
0 |
0 |
1 |
0 |
0 |
0 |
1 |
0 |
| 1 |
1 |
1 |
0 |
0 |
0 |
0 |
0 |
1 |
1 |
1 |
0=false, 1=true.
This truth table covers all Boolean eventualities, but the two green columns (candidates for equivalence) do not match when (p,q,r)=(0,1,0) or (0,1,1). So the proposed equivalence is false.