how to get the correct order on a logic translation?

Question

I'm trying to get the best translation for:

"If today is Tuesday, then I need to make the schedule."

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First I've set:

$T \overset{\wedge}{=}$ "Today is Tuesday"
$S \overset{\wedge}{=}$ "I need to make the schedule"

It leaves us with a few possibilities:

1. $T \Rightarrow S$
2. $S \Rightarrow T$
3. $S \lor T$
4. $S \land T$

I'm not sure which order to take ($S$ or $T$) first. Which would be valid?

Answer 1

As you can see in this Article "A $\Rightarrow$ B" is the connective in propositional calculus which has the meaning "If A is true, then B is also true".

Transferring this knowledge to your question you want to express

If "Today is Tuesday" is true, then "I need to make a schedule" is also true

which is, using your parameters:

$T \Rightarrow S$

Note that $S \Rightarrow T$ would be the correct expression for "If I need to make a schedule, then today is Tuesday" while $S \land T$ $(S \lor T$) would express "Today is Tuesday and (or) I need to make a schedule".
(Annotation: $\lor$ is not exclusive which means that either $T$ or $S$ or both can be true)

As far as $\lor$ and $\land$ are concerned see this Website.

Answer 2

It's number 1 that best translate the statement. Note that the statement does not say that you can make the schedule only on Tuesday. You can make the schedule say on Monday, and that doesn't falsify the statement (this would falsify the statement "If I make the schedule, then is Tuesday", that is the translation to natural language of number 2). What falsify the statement number 1 is when you don't make the schedule on Tuesday. That is the difference between number 2 and 1. The other possibilities: "$\vee$" is natural language "or", "& ($\wedge$)" is natural language "and".