Conditional Premise Proof Problem: Stay in Austin

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Subsection 3.6.3 Conditional Premise Proof Problem: Stay in Austin

Stay in Austin

If Kelly gets her degree, she will get a good job and a good house. If she has a good job she will live in either Palo Alto or Austin. Kelly will not live in Palo Alto. Therefore, if she gets a degree she will live in Austin.

Assign the following names to basic statements:

D : Kelly gets her D egree.

J : Kelly will get a good J ob.

H: Kelly will get a good H ouse.

P : Kelly will live in P alo Alto.

A : Kelly will live in A ustin.

Prove: D → ( J ∧ H ) If Kelly gets degree, she will get a good job and house.

J → ( P ∨ A ) If Kelly has a good job she will live in Palo Alto or Austin.

¬P Kelly will not live in Palo Alto.

∴ D → A If Kelly gets a degree she will live in Austin.

You should try this problem yourself.

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