How to translate the given statement in to propostional formula? " you can have sandwich and salad or  soup "
I was given to translate a given  proposition to propositional formula but i  can not understand where to put parentheses in above statement .
In simple forms it looks like " sandwhich $\land$ salad $\lor$ soup" but  now i know the precedence of "$\land$" is  greater than "$\lor$  so i fromulate it as " (sandwhich $\land$ salad) $\lor$ soup ". which rules out the meaning  that i can have sandwich along with either of the salad or soup ( but not both ) . 
 A: Admittedly, interpreting natural languages can be somewhat ambiguous at times. Following simple rules such as "conjunction takes precedence over disjunction" or "read it from left to right" will not reliably convey the meaning of every statement you come across. Sometimes context helps frame the meaning. At other times, you may need to get some clarification from the source of the statement as to its precise meaning. 
Here is an example of how context could help interpret this statement: when one gets an entree at a restaurant, you are usually given a choice between sides and not allowed to choose all the sides. This would leave us to believe that the disjunction is exclusive and has precedence. In other words,
$h$: you can have a sandwich
$d$: you can have a salad
$p$: you have have a soup
$h \wedge (d \oplus p)\Leftrightarrow h \wedge [(d \vee p) \wedge \neg (d \wedge p)]$
Notice how this contradicts your assumption that conjunction should automatically take precedence, and yet it makes sense intuitively when you consider what is normative culture in a restaurant. For this reason, I suggest getting some clarification from the source of the statement. If this is not available, then I would actually rely on context to guide you. When translating statements from a natural language to a formal one, you must translate them in a way that preserves the original meaning or intent, and I think it's more likely that the meaning of the statement aligns with common everyday experience than otherwise.
