Here is another problem which comes up in transcribing English into logic. Consider the sentence.
(1) Eve is clever and Eve is dark-eyed or Adam is blond.
How do we transcribe this? Should we understand (1) as
(1a) (Eve is clever and Eve is dark-eyed) or Adam is blond.
Or should we understand it as
(1b) Eve is clever and (Eve is dark-eyed or Adam is blond).
As we know from section 1-5, the grouping makes a difference. The problem here is that (1) is bad English. In English we should also indicate the grouping, which we can easily do with a comma. Thus (1a) corresponds to
(1c) Eve is clever and Eve is dark-eyed, or Adam is blond.
and (1b) corresponds to
(1d) Eve is clever, and Eve is dark-eyed or Adam is blond.
Using the following transcription guide
B: Adam is blond.
C: Eve is clever.
D: Eve is dark-eyed.
we get as transcriptions of (1a) and (1c):
And as transcriptions of (1b) and (1d):
Notice that by using parentheses in (1a) and (1b) I have used a mixture of English and sentence logic as an aid to figuring out what seems to be going on. Such mixtures often help in transcription. If you don't see a correct transcription right away, transcribe part, or features of, the English sentence. Then go to work on the parts which you did not transcribe in your first pass at the problem.
The expression 'Either . . . or ' functions in English to indicate grouping in some respects as do parentheses in logic. Anything that goes where you see the '. . .' acts as if it had parentheses around it, even if it is quite complex. (Often something which goes where you see the '-' also acts like it had parentheses around it, but this English device does not always work.) Thus we could write (1a) and (1c) as
(1g) Either Eve is clever and Eve is dark-eyed, or Adam is blond.
'Both . . . and _____' serves much as does 'Either . . . or _____', although the complexities of English grammar don't let you say things such as 'Both Eve is clever and Eve is dark-eyed, or Adam is blond.' To speak grammatical English, one has to say
(1h) Eve is both clever and dark-eyed, or Adam is blond.
which we clearly transcribe as (1e).
Notice that in (1h) we have done some collapsing of English sentence units. When transcribing into logic, you should rewrite 'Eve is clever and dark-eyed.' as a conjunction of two atomic sentences, that is, as 'Eve is clever and Eve is dark-eyed.' or finally as 'C&D'. And, to consider a new example, you should rewrite 'Eve is clever or dark-eyed.' as a disjunction of two atomic sentences, that is, as 'Eve is clever or Eve is dark-eyed.', or finally as 'CvD'.