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A Harder Example - Logical Rule Application

An example of applying a logical rule in a complex scenario, showing step-by-step branching and ordering strategy. Click for more!

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A Harder Example - Logical Rule Application

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  1. A Harder Example (PvQ)>R -[(P>R)&(Q>R)] (PvQ)>R | (P>R)&(Q>R)

  2. A Harder Example (PvQ)>R -[(P>R)&(Q>R)] (PvQ)>R | (P>R)&(Q>R)

  3. A Harder Example (-&) Rule -(A&B) -A -B (PvQ)>R -[(P>R)&(Q>R)] (PvQ)>R | (P>R)&(Q>R)

  4. A Harder Example 1 (-&) Rule -(A&B) -A -B (PvQ)>R -[(P>R)&(Q>R)] -(P>R) -(Q>R) (PvQ)>R | (P>R)&(Q>R)

  5. A Harder Example 1 (PvQ)>R -[(P>R)&(Q>R)] -(P>R) -(Q>R) (PvQ)>R | (P>R)&(Q>R)

  6. A Harder Example 1 (PvQ)>R -[(P>R)&(Q>R)] -(P>R) -(Q>R) (PvQ)>R | (P>R)&(Q>R) (->) Rule -(A>B) A -B

  7. A Harder Example 1 2 (PvQ)>R -[(P>R)&(Q>R)] -(P>R) -(Q>R) (PvQ)>R | (P>R)&(Q>R) (->) Rule -(A>B) A -B P -R

  8. A Harder Example 1 2 (PvQ)>R -[(P>R)&(Q>R)] -(P>R) -(Q>R) (PvQ)>R | (P>R)&(Q>R) (->) Rule -(A>B) A -B P -R

  9. A Harder Example 1 2 3 (PvQ)>R -[(P>R)&(Q>R)] -(P>R) -(Q>R) (PvQ)>R | (P>R)&(Q>R) (->) Rule -(A>B) A -B P -R Q -R

  10. A Harder Example 1 2 3 (PvQ)>R -[(P>R)&(Q>R)] -(P>R) -(Q>R) (PvQ)>R | (P>R)&(Q>R) P -R Q -R

  11. A Harder Example 1 2 3 (>) Rule A>B -A B (PvQ)>R -[(P>R)&(Q>R)] -(P>R) -(Q>R) (PvQ)>R | (P>R)&(Q>R) P -R Q -R

  12. A Harder Example 1 2 3 (>) Rule A>B -A B (PvQ)>R -[(P>R)&(Q>R)] -(P>R) -(Q>R) (PvQ)>R | (P>R)&(Q>R) P -R Q -R THE RESULT OF APPLYINGA RULE MUST APPEAR ONEVERY OPEN BRANCH BELOW THE PLACE IT IS APPLIED.

  13. A Harder Example 1 2 3 4 (>) Rule A>B -A B -(PvQ) R -(PvQ) R (PvQ)>R -[(P>R)&(Q>R)] -(P>R) -(Q>R) (PvQ)>R | (P>R)&(Q>R) P -R Q -R THE RESULT OF APPLYINGA RULE MUST APPEAR ONEVERY OPEN BRANCH BELOW THE PLACE IT IS APPLIED.

  14. A Harder Example 1 2 3 4 -(PvQ) R * -(PvQ) R * (PvQ)>R -[(P>R)&(Q>R)] -(P>R) -(Q>R) (PvQ)>R | (P>R)&(Q>R) P -R Q -R

  15. A Harder Example 1 2 3 4 -(PvQ) R * -(PvQ) R * (PvQ)>R -[(P>R)&(Q>R)] -(P>R) -(Q>R) (PvQ)>R | (P>R)&(Q>R) P -R Q -R

  16. A Harder Example 1 2 3 4 -(PvQ) R * -(PvQ) R * (PvQ)>R -[(P>R)&(Q>R)] -(P>R) -(Q>R) (PvQ)>R | (P>R)&(Q>R) P -R Q -R (-v) Rule -(AvB) -A -B

  17. A Harder Example 1 2 3 4 5 -(PvQ) R * -(PvQ) R * (PvQ)>R -[(P>R)&(Q>R)] -(P>R) -(Q>R) (PvQ)>R | (P>R)&(Q>R) P -R Q -R (-v) Rule -(AvB) -A -B -P -Q

  18. A Harder Example 1 2 3 4 5 -(PvQ) R * -(PvQ) R * (PvQ)>R -[(P>R)&(Q>R)] -(P>R) -(Q>R) (PvQ)>R | (P>R)&(Q>R) P -R Q -R (-v) Rule -(AvB) -A -B -P -Q -(AvB) = -A&-B

  19. A Harder Example 1 2 3 4 5 -(PvQ) R * -(PvQ) R * (PvQ)>R -[(P>R)&(Q>R)] -(P>R) -(Q>R) (PvQ)>R | (P>R)&(Q>R) P -R Q -R (-v) Rule -(AvB) -A -B -P -Q

  20. A Harder Example 1 2 3 4 5 6 -(PvQ) R * -(PvQ) R * (PvQ)>R -[(P>R)&(Q>R)] -(P>R) -(Q>R) (PvQ)>R | (P>R)&(Q>R) P -R Q -R (-v) Rule -(AvB) -A -B -P -Q -P -Q

  21. A Harder Example 1 2 3 4 5 6 -(PvQ) R * -(PvQ) R * (PvQ)>R -[(P>R)&(Q>R)] -(P>R) -(Q>R) (PvQ)>R | (P>R)&(Q>R) P -R Q -R -P -Q * -P -Q *

  22. A Harder Example 5 1 2 3 4 6 -(PvQ) R * -(PvQ) R * (PvQ)>R -[(P>R)&(Q>R)] -(P>R) -(Q>R) (PvQ)>R | (P>R)&(Q>R) VALID P -R Q -R -P -Q * -P -Q *

  23. Ordering Strategy It is best to do non-branching steps first. For more click here

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