Let X be the set of all humans. If x E X, we define the set Ax = {people who had the same breakfast or lunch as x}. (a) Does the collection {Ax :x E X} partition X? Explain your answer.

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7.4.2 Let X be the set of all humans. If x € X, we define the set
Ax =
{people who had the same breakfast or lunch as x}.
(a) Does the collection {Ax : x € X} partition X? Explain your answer.
(b) Is your answer different if the or in the definition of Ax is changed to and?
If Jane and Tom had both had the same breakfast and lunch, then Ajane
fewer distinct sets Ax than there are humans!
=
ATom so there are likely many
Transcribed Image Text:7.4.2 Let X be the set of all humans. If x € X, we define the set Ax = {people who had the same breakfast or lunch as x}. (a) Does the collection {Ax : x € X} partition X? Explain your answer. (b) Is your answer different if the or in the definition of Ax is changed to and? If Jane and Tom had both had the same breakfast and lunch, then Ajane fewer distinct sets Ax than there are humans! = ATom so there are likely many
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