1. Equivalence We have already introduced the idea of equivalence
in discussing translation.

2. Equivalence We have already introduced the idea of equivalence
in discussing translation.
-(AvB) is equivalent to -A&-B.

3. Equivalence We have already introduced the idea of equivalence
in discussing translation.
-(AvB) is equivalent to -A&-B.
A translation exercise is correct if it is equivalent to
an answer I would have chosen.

4. A entails B and B entails A.
Equivalence
A is equivalent to B
iff
A entails B and B entails A.

5. Testing for Equivalence
To show A is equivalent to B ...
with a table: The output rows match.
with a proof: Given A, prove B,
and given B, prove A.
with a tree: The tree for A, -B closes
and the tree for B, -A closes.

6. Examples To show -(PvQ) is equivalent to -P&-Q ...
with a table: The output rows match.
with a proof: Given -(PvQ), prove -P&-Q,
and given -P&-Q, prove -(PvQ).
with a tree: The tree for -(PvQ), -(-P&-Q) closes
and the tree for -P&-Q, --(PvQ) closes.

7. Examples To show -(PvQ) is equivalent to -P&-Q ...
with a table: The output rows match.
P Q (P v Q) -P & -Q
T T F T F F F
F T F T T F F
T F F T F F T
F F T F T T T
* *

8. Examples To show -(PvQ) is equivalent to -P&-Q ...
with a table: The output rows match.
with a proof: Given -(PvQ), prove -P&-Q,
and given -P&-Q, prove -(PvQ).

9. Examples To show -(PvQ) is equivalent to -P&-Q ...
with a table: The output rows match.
with a proof: Given -(PvQ), prove -P&-Q,
and given -P&-Q, prove -(PvQ).
1) -(PvQ) A
2) -P&-Q DM
1) -P&-Q A
2) -(PvQ) DM

10. Examples To show -(PvQ) is equivalent to -P&-Q ...
with a table: The output rows match.
with a proof: Given -(PvQ), prove -P&-Q,
and given -P&-Q, prove -(PvQ).
with a tree: The tree for -(PvQ), -(-P&-Q) closes
and the tree for -P&-Q, --(PvQ) closes.

11. Examples To show -(PvQ) is equivalent to -P&-Q ...
with a table: The output rows match.
with a proof: Given -(PvQ), prove -P&-Q,
and given -P&-Q, prove -(PvQ).
with a tree: The tree for -(PvQ), -(-P&-Q) closes
and the tree for -P&-Q, --(PvQ) closes.
-P&-Q
--(PvQ) -P -Q
PvQ
P Q
* *
-(PvQ)
-(-P&-Q) -P -Q
--P Q
* *

12. For more click here Summary of the Tests
To show A is equivalent to B ...
with a table: The output rows match.
with a proof: Given A, prove B,
and given B, prove A.
with a tree: The tree for A, -B closes
and the tree for B, -A closes.
For more click here