Question

MATH ............................................

Answer 1

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 $a\implies b$, because Rome is inside Italy, and similarly $b\implies c$, because Italy is a European state.

So, if I live in Rome, I must live in Europe as well.