Interval and set builder notation?

Is this correct, i'm so confused so if it's completely wrong... bear with me.

1. x is less than or equal to 2 OR 3<x<5

I put [-infiniti,5]

2. number between 1 and to

IV: [1,10]

SB: {x|1<x<10}

3. x does not equal five (= sign w/ slash through it) and x less than or equal to 10

i have no idea to go about that

can you plz tell me if i'm a. doing them right b. what i'm doing wrong c. how to fix it c. explanation

im not asking for the answer i just need to know how to do it than you!

Update:

yes sorry didnt realize that but the question says numbers between 1 nd 10

1 Answer

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  • 10 years ago
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    As for the first one, I agree the set of all x such that " x is less than or equal to 2 or 3 < x < 5" will include all x from - infinity to 5. But it won't be inclusive at either end. That is, it doesn't included 5, and it doesn't include - infinity. You'll never want to actually include + or - infinity in your sets. So instead of

    [-∞,5]

    you should have (-∞, 5). Remember that brackets "[" mean included whereas parenthesis "(" indicate that the end is not included.

    As for the second one, I'm a little confused. Is that supposed to read "number between 1 and ten"? If so, it's quite a weak statement, because it doesn't indicate if 1 and 10 should be included or not. Usually, when someone says something like "a number between 1 and 10" they only mean integers 1,2,3,4,5,6,7,8,9,10. Whoever wrote that question did not do so clearly.

    The two answers you have for that are not the same.

    {x| 1 < x < 10}

    would be (1,10) in interval notation. [1,10] would be {x| 1 ≤ x ≤ 10} in set notation.

    As for number three, the set of all x less than or equal to 10 would be

    {x| x ≤ 10} or (-∞, 10].

    But you need 5 to be excluded. You can do this by having your set be everything from - infinity up to (not including) 5, then everything from 5 to 10.

    (-∞, 5) U (5, 10]

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