# I Logically equivalent

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1. May 2, 2016

### The Subject

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
$$(P \to Q) \lor (P \to R) \\ (P \lor \neg Q) \lor (P \lor \neg R) \\ P \lor \neg Q \lor \neg R \\ P \lor \neg(Q \land R) \\ P \to (Q \land R)$$
and
$$P \to (Q \lor R) \\ P \lor \neg(Q \lor R ) \\ P \lor (\neg Q \land \neg R) \\ (P \lor \neg Q) \land (P \lor \neg R) \\ (P \to Q) \land (P \to R)$$

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

2. May 2, 2016

### andrewkirk

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. May 2, 2016

### The Subject

AHHHH thank you!