im having a difficulty translating it to english. SO basically, i will type the corresponding statements in words.
(Universal x ( x is not 0) -> existential y(xy = 1)
then we need to evaluate it as true or false.
heres my approach. i translated it to english as :
" For some x OR some y, xy = 1 is valid. " and my evaluation is "true" (T)
The reason why there is an or because i converted the "p->q" into simpler operations (negate p, or q). Then negate q means negating the universal x so i made it to some x.
I hope things get sorted out if Im wrong. Thanks stackexchange
Best Answer
It seems to me a bit unclear what does "for some $x$ OR some $y$" mean? Can you have $xy$ without choosing an $x$, for example?
In this case, translating the implication to conjunction does not change the quantifiers: "$\forall$x.$\exists$y.$\neg[(x\neq0)\wedge(xy\neq1)]$". So now, using De Morgan: $\forall$x.$\exists$y.$[(x=0)\vee(xy=1)]$.
The law of translation is $(p \implies q) \equiv \neg(p \wedge\neg q)$.
However, why not try translating it directly? I think you will find it much less confusing.