Hi. I couldn't solve my problem because it has two conditional logical propositions. The problem is:
can anyone help me about this, thanks =)
Hello, dpb!
We're expected to know that: .$\displaystyle a \to b$ is equivalent to $\displaystyle \sim a \vee b$
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 . . .