# CLASS-7OVERLAPPING SET

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  Z is overlapping set and  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