Question

Can someone Exxon how this can be written in inter notation and set-builder notation


Numbers within 3 units of. 2

Answer 1

Let me Exxon: What are the numbers exactly 3 units away from 2? These are the boundaries of your interval. They are given by 2-3 and 2+3, or -1 and 5. So all the numbers within 3 units of 2 is equivalent to asking for all the numbers between -1 and 5. In interval notation we can write this as [-1,5]. I use the [] brackets instead of the () brackets because your interval includes the numbers at the boundaries. If I used the () brackets, then that would imply that you were NOT including the boundaries of the interval in your SET of numbers within 3 units of 2. Now, how would we write this in set-builder notation? There are actually multiple ways to do this, I will explain the way I would do it and then the way your teacher probably wants you to. Set builder notation is written like this:

{ variable | condition for inclusion in your set }

So we can pick any variable to represent the elements of your set, but I'll pick x. Now what are the conditions, that a given value of x is in your set? Well the conditions were given to you in the question: x must be a number within 3 units of 2. But I have already shown that this is equivalent to saying that x must be in the interval [-1,5]. So the way I would answer this is:

{ x | x in [-1,5]}

Now, saying that x is in the interval [-1,5] is equivalent to saying that -1 <= x <= 5, where "<=" is the same as "less than or equal to", so I could rewrite this statement as:

{ x | -1 <= x <= 5}

This is probably the form your teacher wants to see. Hope that helps!

Answer 2

Thank you so much you helped a lot !!

Answer 3

How would I write positive odd numbers in set builder notation