It must be true that a implies c, because of the transitive property.
If a is true, then b is true as well. But every time b is true, c is true as well.
So, "jumping" over b, we have that if a is true, c is true as well.
Think of this example:
- a: I live in Rome
- b: I live in Italy
- c: I live in Europe
It is true that [tex]a\implies b[/tex], because Rome is inside Italy, and similarly [tex]b\implies c[/tex], because Italy is a European state.
So, if I live in Rome, I must live in Europe as well.
