anonymous
  • anonymous
Consider the set D of all numbers in the interval (-infinity , 5). What is the complement of D ?
Mathematics
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SOLVED
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chestercat
  • chestercat
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anonymous
  • anonymous
I think it's (5, +infinity) . I've never see it .
anonymous
  • anonymous
The first is the set: \[\{x\in R\phantom{.}|\phantom{.}x\in (-\infty,5)\}\] The complement would be the rest of the number line from \(5\) to \(+\infty\) which is notated as : \[\{x\in R\phantom{.}|\phantom{.}x\in (5,\infty)\}\]
anonymous
  • anonymous
The choices are A.(-∞,-5) B.[5,+∞) C.(-∞,5) D.(5+∞)

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anonymous
  • anonymous
OOOOOH Well we know that \(5\) and \(+\infty\) are part of the interval so we are given the options of: \([5,+\infty)\) and \((5,+\infty)\) EXACTLY, how as the original set notated?
anonymous
  • anonymous
I typed B & D the way it was on my paper . :c
anonymous
  • anonymous
Haha no like the original set not the complement, the one from negative infinity to 5
anonymous
  • anonymous
Like did it have two brackets like this: \((\phantom{...})\)?
anonymous
  • anonymous
Everything that's on here is what's on the paper , & Yeah it was (-∞,5)
mathstudent55
  • mathstudent55
Set D does not include5, so the complement must include 5: D': \([5, \infty) \) The answer is B.
mathstudent55
  • mathstudent55
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anonymous
  • anonymous
Yeahhh that's all I was wondering because if the orginal set included or discluded the "5" by having either a "\(]\)" or a "\()\)" makes a difference in the answer but Math student 55 is correct in saying that in THAT case, he answer is B
anonymous
  • anonymous
Oh okay , I understand . Thank you guys ! :D
anonymous
  • anonymous
Anytime Sceenie!
mathstudent55
  • mathstudent55
The word for not including is "excluded" although I like your new word "discluded." The description of D is \( (-\infty, 5) \). The parentheses to the right of 5 means that 5 is excluded ("discluded"). The complement is the set that includes everything that is not in D, so 5 must be included. That's why you get \( [5, +\infty) \). The reason we use parentheses with infinity and not square brackets is by convention. Infinity is not a number. For example, we write \( (-\infty, -8] \) and \( (3, \infty) \), and not \( [-\infty, -8] \) and \( (3, \infty] \).

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