One could use the phrase "and/or" (wikipedia) which describes this logical structure. Note that it is considered ugly by many English usage style guides (the legal commentaries on "and/or" are quite amusing from the wikipedia link).
Wikipedia's style guide suggests "a or b, or both" for this logical structure.
a || b can also be read of "at least one of a or b" which has a reasonable flow to the phrase. This covers the "one must be true, but both may be true too" case with only slight awkwardness and doesn't encumber the reader with trying to figure out what is the correct interpretation of the logical structure that the "a or b, or both" (there are two 'or' statements in there that can require pause to think about what is meant).
The "at least one of ..." phrasing also makes it easy to adapt to the n-ary or statement such as
a || b || c || d which can then be written as "at least one of a, b, c, or d."
Note that these logic to English translations really only work well when the logical statement is not too complex. Trying to transcribe
(a && b) || c || (d && e) into text leads to a complex statement that doesn't have a clean idiomatic phrase in English.