hi

Here is a problem I am trying to do from Kenneth Rosen's

"Discrete mathematics..."

Show that

is a tautology whenever are propositions, whenever

Here is the proof I attempted.

Base Case:

let be arbitrary propositions.Now consider

To prove this, we assume antecedent and since the antecedent is same

as consequent, it proves the above compound proposition . So

.

Induction case: Let be arbitrary. Also suppose

. To prove , take arbitrary

propositions . We have to prove

that

is a tautology. In other words, we have to prove it. Since its an implication,

we suppose

and we also suppose that

It follows that, in particular,

and

So by modus ponens, we have

which proves

Since n is arbitrary, result holds generally.

Is it correct reasoning ?

Thanks