LEARN MATH STEP BY STEP THROUGH VERY EASY PROCESS

INTERSECTION OF TWO SETS

__Intersection of two Sets__

**The intersection of two sets X & Y is the set of all
members which belongs to both X & Y. It is denoted by X ****⋂**** Y, which
is to be read as “ X intersect Y ” thus, x ****ϵ**** X ****⋂**** Y if x ****ϵ**** X and x ****ϵ**** Y**

__Example– 1__

**Let, X = { 1, 2, 3 } , Y = { 4, 5, 6, 7 } and Z = { 6,
7, 8, 9, 10 }**

** Then, X ****⋂**** Y = { 1,
2, 3 } ****⋂**** { 4, 5, 6, 7 } = ****φ, because there is no member of X
belongs to Y**

**
X ****⋂**** Z =
{ 1, 2, 3 } ****⋂**** { 6, 7, 8, 9, 10 } = ****φ , because there is no member of X
belongs to Z**

**
Y ****⋂**** Z =
{ 4, 5, 6, 7 } ****⋂**** { 6, 7, 8, 9, 10 } = { 6, 7 } **

** **

__Example– 2__

**If, X = { x / x is a digit of 452372 } and Y = { x / x is a
digit 2047 } then find X ****⋂**** Y**

**Ans.) X = { x / x is a digit of 452372 }**

** => X = { 4, 5, 2, 3, 7 } (
Writing the tabular form)**

** Y = { x / x is a digit 2047 } **

** => Y = { 2, 0, 4, 7
} ( Writing the tabular form)**

**Now, X ****⋂**** Y = { 4, 5, 2, 3, 7 } ****⋂**** { 2, 0,
4, 7 } = { 2, 4, 7 }**

** **

__Example– 3__

**Find the number of the set n( X ****⋂**** Y
), If ****, X = { x / x is a digit of 452372 } and Y = { x / x is
a digit 2047 }**

**Ans. ) X = { x / x is a digit of 452372 }**

** => X = { 4, 5, 2, 3, 7 } (
Writing the tabular form)**

** Y = { x / x is a digit 2047 } **

** => Y = { 2, 0, 4, 7
} ( Writing the tabular form)**

**Now, X ****⋂**** Y = { 4, 5, 2, 3, 7 } ****⋂**** { 2, 0,
4, 7 } = { 2, 4, 7 }**

**Now, n( X ****⋂**** Y ) = { 2, 4, 7 } = ****3**