Inclusion-Exclusion Principle in Combinatorics
Set X has terms {183, 294, 375, 535, 638, 750, 920}.
Set Y has terms {375, 450, 535, 725, 700, 750, 825}.
What is the intersection of X and Y?
Incorrect.
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This set contains a value that is not in both sets, so it cannot be the intersection of these two sets. 920 is only in X, not Y.
Incorrect.
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This set does not include the entire intersection of X and Y.
Correct.
The intersection of X and Y is the set of all elements that are members of both sets. The answer should include any number that appears in the two sets, and not include any other number
Set X has terms {183, 294, 375, 535, 638, 750, 920}.
Set Y has terms {375, 450, 535, 725, 700, 750, 825}.
The terms that are in both X and Y—375, 535, and 750—are the only terms that should be included in the intersection set.
$$\displaystyle X \bigcap Y = 375, 535, 750$$
Incorrect.
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This set contains all of the terms that are in only X or only Y, but does not contain any of the terms that are in the intersection of X and Y.
Incorrect.
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This choice is the _union_ of X and Y $$(X \bigcup Y)$$ not the _intersection_ of X and Y $$(X \bigcap Y)$$.
You are looking for the intersection, which only includes terms that occur in both sets.
{375, 750}
{375, 535, 750}
{375, 535, 750, 920}
{183, 294, 450, 638, 725, 700, 825, 920}
{183, 294, 375, 450, 535, 638, 725, 700, 750, 825, 920}
