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

can anyone help me about this, thanks =)

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- Sep 26th 2007, 02:25 PMdpbLogic 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

can anyone help me about this, thanks =) - Sep 26th 2007, 04:55 PMSoroban
Hello, dpb!

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

Quote:

Find a logically equivalent proposition for:

. . $\displaystyle (p \vee q) \to (\sim p \to q)$

by first writing its contrapositive, and then applying DeMorgan's law

and the equality for $\displaystyle \sim(p \to q)$

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

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

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 . . .

- Sep 27th 2007, 10:00 AMdpb
thanks =)