Well one of my Algebra questions asks for the intersection of two intervals which are [-6,6] and [1,13] and if the intersection is empty type empty. This is so confusing to me. Can someone please help. Thank You.
Thank you for the opportunity to help you with your question!
Let me begin by explaining the basic idea of an interval. If an interval (Let us call it Interval A) is defined as [-6,6] then it means that Interval contains all the possible values which are lying in between -6 and 6 ( including the numbers -6 and 6). To illustrate, some examples of numbers belonging to Interval A would be -3, 0. 4, 4.3, etc.
Similarly, [1,13] then it means that the interval contains all the possible values which are lying in between 1 and 13 ( including the numbers 1 and 13). Let us call this Interval B.
Now, an intersection of the Interval A and Interval B is asked. An intersection of two intervals is basically another set of numbers, which has the collection of all the possible numbers that belong to both Interval A and Interval B simultaneously. Let us call the Intersection 'C'.
Look at the number lines for Intervals A and B. It becomes easier to visualise the numbers common to both the intervals.
Clearly the numbers belonging to both the intervals, simultaneously have to be greater than 1, but less than 6.
Hence the intersection, 'C' is the Interval [1,6]
An intersection of two intervals is empty when the two intervals have no common numbers. For eg, the intervals [1,5] and [8,9] do not have any common numbers and hence the intersection of these two sets would be an empty set.
There fore in the question given in you assignment, the intersection of the two sets [-6,6] and [1,13] is not empty.
Please let me know if you need any clarification. I'm always happy to answer your questions. Hope you find my answer satisfactory. Rate me 5. :)
The union of two sets is the set of all the numbers that belongs to any one or both of the sets. In case of the sets [-6,6] and [1,13] the union is the interval [-6,13]. Hope you find this satisfactory! :)
Oct 14th, 2015
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