Overlapping Set
If, X ⋂ Y ≠ φ when X ⋂ Y has at least one member then two sets X & Y are called overlapping set. Clearly, if two sets are not overlapping then both the set X & Y are called disjoint set and the disjoint set is also called a non-overlapping set.
Example– 1
Let, X = { 5, 6, 7, 8 }, Y = { 10, 12, 14, 16, 18 }, Z = { 14, 15, 16, 17, 18, 19, 20 }
Verify Y ⋂ Z is overlapping set and X ⋂ Y is non-overlapping set
Ans.) Y ⋂ Z = { 10, 12, 14, 16, 18 } ⋂ { 14, 15, 16, 17, 18, 19, 20 } = { 14, 16, 18 } ≠ φ, so Y & Z are overlapping set.
And, X ⋂ Y = { 5, 6, 7, 8 } ⋂ { 10, 12, 14, 16, 18 } = φ, so X & Y are non-overlapping set
Example– 2
Let, X = { x / x is a prime factor of 350 }, Y = { 1, 2, 3, 4, 5 } & Z = { 2, 4, 6, 8, 10 },
Verify X & Y , X & Z and Y & Z are overlapping
Ans.) writing in the tabular form, X = { 2, 5, 7 }
So, X ⋂ Y = { 2, 5, 7 } ⋂ { 1, 2, 3, 4, 5 } = { 2, 5 } ≠ φ, so X & Y are overlapping set.
So, X ⋂ Z = { 2, 5, 7 } ⋂ { 2, 4, 6, 8, 10 } = { 2 } ≠ φ, so X & Z are overlapping set
And, Y ⋂ Z = { 1, 2, 3, 4, 5 } ⋂ { 2, 4, 6, 8, 10 } = { 2, 4 } ≠ φ, so Y & Z are overlapping set