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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

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Solution

(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.


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