People Who Like A or C: Subset of Those Who Don't Like B and C

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The discussion revolves around rephrasing the relationship between sets of people who like certain preferences. The original statement suggests that those who like A or C form a subset of those who do not like both B and C. Participants are trying to clarify the logical connections between these groups, specifically focusing on the implications of liking A or C in relation to disliking B and C. The formulation attempts to express that liking A or C means not liking both B and C. Overall, the conversation seeks to accurately articulate these set relationships in clear English.
EvLer
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I have trouble re-wording this statement in English:
(A u C) is a subset of (B n C)'

where A = {people who like A}
B = {people who like B}
C = {people who like C}

I know that A subs. of B <=> B' subs. of A', but that does not seem to help;

so far my formulation is following (it is probably inaccurate):

people who like A or C or both are people who don't like both B and C;
or
people who like A or C or both are people who like neither B nor C;
:confused:

Thanks in advance.
 
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Your first statement seems correct to me.

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