How to check which part is the hypotheses and which part is conclusion in any conditional statement? If any statement have some keywords like "if...,then...." "only if", "whenever", "unless", "is sufficient", "is necessary" etc present in any statement then I am able to determine which part is the hypotheses and which one is conclusion. But in a sentence like this:
You only eat what tastes good
$E(x)$ = you eat $x$
$T(x)$ = $x$ tastes good
domain of x consists all foods
I understand this sentence can be expressed in a conditional form like this (correct me if I wrong)
$\forall x (E(x) \rightarrow T(x))$
or,
$\forall x (T(x) \rightarrow E(x))$
But I my problem is , which one is correct? How can I determine which one is the hypotheses and which one is the conclusion of a conditional proposition like this where no keyword like "if then" etc are not used?
The two sentences you wrote mean, in order,
Your first one, $\forall x(E(x)\to T(x))$, says that for any piece of food ever, if you eat it, that means it tastes good. Which is what you're after.
The second one, $\forall x(T(x)\to E(x))$, says that for any piece of food ever, if it tastes good, you eat it. Which 1) means that you're going to be very full, very fast, and 2) doesn't say anything about what you do with non-tasty food. You might eat it, you might not, we don't know. So that's not the one you're after.
When you have the sentence $E(x)\to T(x)$, it means, in plain English, "If $E(x)$, then $T(x)$". Which has the same meaning as "$E(x)$ only if $T(x)$". In other words, there is no way $E(x)$ is true but not $T(x)$.