Question

# 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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