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Given:U = {x|0 < x < 10 and x is an integer}S = {x|0 < x < 10 and x is an odd integer}The complement of set S within the universal set U isA{0, 2, 4, 6, 8, 10}B.{2, 4, 6, 8, 10}C. {0, 2, 4, 6, 8}D. {2, 4, 6, 8}



Answer :

Notice that set U is formed by all integers between 0 and 10.

Set S is formed by all odd integers between 0 and 10.

Remember that the complement of a set is all elements inside the universe but out of that set. So, in this case, we have to find all elements that do not belong to S but to the universal set U which would be all the even numbers between 0 and 10.

Therefore, the complement of S is

[tex]\mleft\lbrace2,4,6,8\mright\rbrace[/tex]

Notice that we can't include 10 because the set is not defined for that number since is an open interval.

The right answer is D.

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