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

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SUMMARY

The discussion centers on the logical relationship between sets of people based on their preferences for items A, B, and C. Specifically, it establishes that the union of sets A and C (people who like A or C) is a subset of the intersection of sets B and C (people who like both B and C). The participant seeks clarification on rephrasing this relationship accurately in English, ultimately concluding that those who like A or C do not like both B and C.

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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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