Connotation of 行きますか vs 行きましょうか


My textbook has the following conversation:

> A: 明日どこに行きますか。
>
> B: デパートに行きましょう。
>
> A: どのデパートに行きますか。
>
> B: 貴方の家の北のデパートに行きましょう

The third line is translated to English in the textbook as "which department
store should we go to?" My trouble is with the connotation of this sentence.

I think that the 〜ます stem seems to imply a certainty expected upon B, that is,
that B already knows where we're going. In English I would expect this more to
be "which department store are we going to?" The "should we go to" seems to me
to ask for suggestions (rather than a unilateral decision by B). If that
connotation is what is desired, then I think that the third line would be
better written as どのデパートに行きましょうか。

Am I wrong about the connotation of this sentence, or am I right in thinking
that the 〜ます stem is implying a stronger level of certainty from B than
expected?




You're correct in thinking that "B" is not giving a direct certainty in the
form of "We will go to X". However, in this context, the suggestion is a more
explicit suggestion than "Should we go to X" as if it were a question. It's
probably closer to "Let's go to X" as opposed to "We will go to X". So,
applying that level of suggestion, let's translate the example:

> A: 明日どこに行きますか。  
>  A: Where are we going tomorrow?
>
> B: デパートに **行きましょう** 。  
>  B: **Let's go** to a department store.
>
> A: どのデパートに行きますか。  
>  A: Which department store will we go to?
>
> B: 貴方の家の北のデパートに **行きましょう**  
>  B: **Let's go** to the department store north of your house.




You're correct in thinking that "B" is not giving a direct certainty in the
form of "We will go to X". However, in this context, the suggestion is a more
explicit suggestion than "Should we go to X" as if it were a question. It's
probably closer to "Let's go to X" as opposed to "We will go to X". So,
applying that level of suggestion, let's translate the example:

> A: 明日どこに行きますか。  
>  A: Where are we going tomorrow?
>
> B: デパートに **行きましょう** 。  
>  B: **Let's go** to a department store.
>
> A: どのデパートに行きますか。  
>  A: Which department store will we go to?
>
> B: 貴方の家の北のデパートに **行きましょう**  
>  B: **Let's go** to the department store north of your house.

