Logically equivalent

  • #1
From the text it says (P -> Q) or (P -> R) is equivalent to P -> (Q or R)

I tried to see if this is true so I tried
[tex] (P \to Q) \lor (P \to R) \\
(P \lor \neg Q) \lor (P \lor \neg R) \\
P \lor \neg Q \lor \neg R \\
P \lor \neg(Q \land R) \\
P \to (Q \land R) [/tex]
and
[tex] P \to (Q \lor R) \\
P \lor \neg(Q \lor R ) \\
P \lor (\neg Q \land \neg R) \\
(P \lor \neg Q) \land (P \lor \neg R) \\
(P \to Q) \land (P \to R) [/tex]

From what I've done its seems like they're not equivalent ?!?!?
 

Answers and Replies

  • #2
andrewkirk
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I tried
[tex] (P \to Q) \lor (P \to R) \\
(P \lor \neg Q) \lor (P \lor \neg R) [/tex]
The second line does not follow from the first.

I think what you meant to write for the second line was
$$(\neg P\vee Q)\vee (\neg P\vee R)$$
which is not the same thing.
 
  • #3
The second line does not follow from the first.

I think what you meant to write for the second line was
$$(\neg P\vee Q)\vee (\neg P\vee R)$$
which is not the same thing.

AHHHH thank you!
 

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