8.Which of the following pairs of sets are disjointG) 1, 2, 3, 4) and (x:x is a natural number and 4 3xs6)(i) a, e, i, o, u and c, d, e, f )(iii) Ix:x is an even integer ) and {x: x is an odd integer)
(i)
Given sets are { 1 , 2 , 3 , 4 } and { 4 , 5 , 6 }
The two sets are called disjoint sets if they have no common elements between them.
The intersection between the sets { 1 , 2 , 3 , 4 } and { 4 , 5 , 6 } is taken.
= { 1 , 2 , 3 , 4 } ∩ { 4 , 5 , 6 } = { 4 } ≠ ϕ
As, there is a common element between both the sets, it cannot be called as disjoint set.
Therefore, this pair of sets is not a disjoint set.
(ii)
Given sets are { a , e , i , o , u } and { c , d , e , f } .
The two sets are called disjoint sets if they have no common elements between them.
The intersection between the sets { a , e , i , o , u } and { c , d , e , f } is taken.
= { a , e , i , o , u } ∩ { c , d , e , f } = { e } ≠ ϕ
As, there is a common element between both the sets, it cannot be called as disjoint set.
Therefore, this pair of sets is not a disjoint set.
(iii)
Given sets are { 2 , 4 , 6 , 8 , ... } and { 1 , 3 , 5 , 7 , ... } .
The two sets are called disjoint sets if they have no common elements between them.
The intersection between the sets { 2 , 4 , 6 , 8 , ... } and { 1 , 3 , 5 , 7 , ... } is taken.
= { 2 , 4 , 6 , 8 , ... } ∩ { 1 , 3 , 5 , 7 , ... } = ϕ = ϕ
As, there is no common element between both the sets, it is a disjoint set.
Therefore, this pair of sets is a disjoint set.
(i)
Given sets are
The two sets are called disjoint sets if they have no common elements between them.
The intersection between the sets
As, there is a common element between both the sets, it cannot be called as disjoint set.
Therefore, this pair of sets is not a disjoint set.
(ii)
Given sets are
The two sets are called disjoint sets if they have no common elements between them.
The intersection between the sets
As, there is a common element between both the sets, it cannot be called as disjoint set.
Therefore, this pair of sets is not a disjoint set.
(iii)
Given sets are
The two sets are called disjoint sets if they have no common elements between them.
The intersection between the sets
As, there is no common element between both the sets, it is a disjoint set.
Therefore, this pair of sets is a disjoint set.
