12. State whether each of the following statement is true or false. Justify your answer(i) {2,3, 4, 5 ] and 3, 6) are disjoint sets.(ii) t a, e, i, o, u | and { a, b, c, d jare disjoint sets(iii) { 2, 6, 10, 14 } and { 3, 7, 11, 15} are disjoint sets.(iv) 2,6, 10 ) and 3, 7, 11] are disjoint sets
(i)
Given sets are { 2 , 3 , 4 , 5 } and { 3 , 6 }
The two sets are called disjoint sets if they have no common elements between them.
The intersection between the sets { 2 , 3 , 4 , 5 } and { 3 , 6 } is:
= { 2 , 3 , 4 , 5 } ∩ { 3 , 6 } = { 3 } ≠ ϕ
As there is a common element between the sets, they cannot be called disjoint sets.
Hence, it is a FALSE statement.
(ii)
Given sets are { a , e , i , o , u } and { a , b , c , d }
The intersection between the sets { a , e , i , o , u } and { a , b , c , d } is
= { a , e , i , o , u } ∩ { a , b , c , d } = { a } ≠ ϕ
As there is a common element between the sets, they cannot be called disjoint sets.
Hence, it is a FALSE statement.
(iii)
Given sets are { 2 , 6 , 10 , 14 } and { 3 , 7 , 11 , 15 }
The intersection between the sets { 2 , 6 , 10 , 14 } and { 3 , 7 , 11 , 15 } is
= { 2 , 6 , 10 , 14 } ∩ { 3 , 7 , 11 , 15 } = ϕ
As there is no common element between the sets, they are disjoint sets.
Hence, it is a TRUE statement.
(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 the sets, they cannot be called disjoint sets.
Hence, it is a FALSE statement.
(ii)
Given sets are
The intersection between the sets
As there is a common element between the sets, they cannot be called disjoint sets.
Hence, it is a FALSE statement.
(iii)
Given sets are
The intersection between the sets
As there is no common element between the sets, they are disjoint sets.
Hence, it is a TRUE statement.
