Union Of Two Sets
The union of two sets ‘X’ & ‘Y’ is the set of all members which belong to ‘X’ or ‘Y’ or to both the sets. If all members which belongs to ‘X’ or ‘Y’, then it can be denoted by X ⋃ Y and it must be read as X union Y, if x is a member of both or either X or Y then it can be written as x ϵ X ⋃ 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 } = { 1, 2, 3, 4, 5, 6, 7 }
X ⋃ Z = { 1, 2, 3 } ⋃ { 6, 7, 8, 9, 10 } = { 1, 2, 3, 6, 7, 8, 9, 10 }
Y ⋃ Z = { 4, 5, 6, 7 } ⋃ { 6, 7, 8, 9, 10 } = { 4, 5, 6, 7, 8, 9, 10 }
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 } = { 0, 2, 3, 4, 5, 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 } = { 0, 2, 3, 4, 5, 7 }
Now, n (X ⋃ Y) = 6