word choice - When should we use "and" and/or "and/or"?

What's the difference between "and" and "and/or"?

How do we decide whether to use one or the other?

_{Note: Also it would be great if someone could explain how do we actually pronounce "and/or" verbally in a sentence...}

Answer

Breaking this down:

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  and/or is as official as English gets in the sense that you can use it in extremely formal contexts. There is typically a better way to say whatever is being said but it does convey a specific meaning.

  
  


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  You should use and/or when both options are applicable in its place. "I would like cake and/or pie" means "I would like one or both of the following: cake; pie."

  
  


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  The main reason for using and/or is to remove the ambiguity of whether and means "only both" and whether or means "only one." And/or explicitly means "it could be one of these or both of these."

  
  


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  The confusion is drastically exacerbated by mathematicians, logicians and/or computer scientists who are very familiar with the differences between the logical operators AND, OR, and XOR. Namely, or in English can be either OR or XOR; and/or can only mean OR. As you may have noticed, all of the terms look similar which leads to the confusion in parsing sentences like your title.

  
  

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EDIT: To strictly answer the question, you should use A and B when you explicitly mean both A and B, and you should use A and/or B when you mean A or B (or both).

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In response to a request for pronunciation, I typically treat the / as a hyphen and simply say "and or". This is not always standard for the / symbol, however, and other words or phrases with a / may be different.