Semantic Tree of Negated Conditional Statement

[Horse]

Homework Statement

Show the semantic tree of:

$$\neg ( ( p_0 \rightarrow p_1 ) \rightarrow \neg ( p_1 \rightarrow p_2 ) )$$

Homework Equations

$$\neg ( ( p_0 \rightarrow p_1 ) \rightarrow \neg ( p_1 \rightarrow p_2 ) )$$

The Attempt at a Solution

I cannot understand its purpose. Where should you start?

 

[Mark44]

The term "semantic tree" doesn't ring any bells with me in the context of logical statements. Do you have any worked examples in your notes or text?

What I would try (and I have no idea if this is the right thing to do), is to make a table with T and F values for p₀, p₁, and p₂ -- eight rows will do the trick. In the same table, calculate the values of p₀ ==> p₁, p₁ ==> p₂, and so on with the negated expressions, and see what I get from that.

 

[Horse]

Semantic tree,... tree proof.

The word is "tree proof". You can see that it is valid:

http://www.umsu.de/logik/trees/?f=(... \rightarrow \neg (\forallb\forallcPb\toPc)))))

Solved :)