LEARN MATH STEP BY STEP THROUGH VERY EASY PROCESS

OVERLAPPING 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 ****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**