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Equivalence

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

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Equivalence

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  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. 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) -P&-Q A 2) -(PvQ) 1 DM 1) -(PvQ) A 2) -P&-Q 1 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 -(PvQ) -(-P&-Q) -P -Q --P --Q * * 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 * *

  12. 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

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