# CLASS-7INTERSECTION 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