Conditional Premise Proof Problem: Party

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Subsection 3.6.2 Conditional Premise Proof Problem: Party

Party:

If we come home early and then, if we go to sleep early, we will get up early. Either we will come home early or we will go to the party. In either case, we will go to sleep early. Therefore, if we do not go to the party, we will get up early.

Assign the following names to basic statements:

H : We come H ome early.

S : We go to S leep early.

U: We will get U p early.

P : We will go to the P arty.

Prove : H → ( S → U) If we come home early, and then if we go to sleep early, we will get up early.

H ∨ P Either we will come home early or we will go to the party.

S We will go to sleep early.

¬ P → U If we do not go to the party, we will get up early.

You should do this proof yourself.

You can also watch our video, which will outline a strategy for creating a proof.