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