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Intersection of Open Sets

TopOpen Set is a collection or group of objects, which include values in certain range except its minimum and maximum value like we have a set of Integer Numbers, which include all integers from 1 to 100 except 1 and 100 then open set is (1, 100). If we want to include some similar properties from two open Sets, we use Intersection of open sets method like we have a set of real number R = (1, 2, 7) and a set of rational number Z = (1/3, 1, 3/5, 2/5), then intersection of these open set is,
R ∩ Z = (1, 2, 7) ∩ (1/3, 1, 3/5, 2/5) = (1),
So, we can say that intersection of open sets always produce an open set and always produce a common numbers between given sets.
For calculating the intersection of open sets we use following steps -
Step 1: First of all, we analyze both set, which we want to intersect like we have a set of integer and another set is a set of irrational number, then intersection of both these set is null because there is no connection between them.
Step 2: After evaluation of both sets, we collect common numbers from both these sets means an intersection of open sets always produce common numbers from both these sets -
A ∩ B = (common numbers),
Now we will take an example, for understanding the process of intersection of open sets:
Example: Find an intersection of open sets, where one open set is X = (3, 4, 5, 6, 7) and another open set Y = (6, 7, 8, 9)?
Solution: Here we use above two steps for evaluating the intersection of given open sets -
X ∩ Y = (3, 4, 5, 6, 7) ∩ (6, 7, 8, 9) = (6, 7).
So, intersection of ‘X’ and ‘Y’ is (6, 7).