# Logic Question

• September 26th 2007, 02:25 PM
dpb
Logic Question
Hi. I couldn't solve my problem because it has two conditional logical propositions. The problem is:
http://img407.imageshack.us/img407/6...estion2vd4.jpg

• September 26th 2007, 04:55 PM
Soroban
Hello, dpb!

We're expected to know that: . $a \to b$ is equivalent to $\sim a \vee b$

Quote:

Find a logically equivalent proposition for:
. . $(p \vee q) \to (\sim p \to q)$

by first writing its contrapositive, and then applying DeMorgan's law
and the equality for $\sim(p \to q)$

They were trying to be helpful by outlining the steps we should follow,
. . but I think they made it more confusing.
I don't see the purpose of using the contrapositive here.
. . I wouldn't have done it that way.
Besides, the statement is a tautology . . .

Contrapositive: . $\sim(\sim p \,\to \,q) \to \sim(p \vee q)$

which gives us: . $\sim(p \vee q) \,\to \,\sim(p \vee q)$

And this is a tautology: "a thing implies itself" ... which is always true.
I don't know of any "logically equivalent proposition" we can write . . .

• September 27th 2007, 10:00 AM
dpb
thanks =)