i) {2,3,4,5} and {3,6} are disjoint sets.

Question

State whether each of the following statement is true or false. Justify your answers. 

i) {2,3,4,5} and {3,6} are disjoint sets. 

ii) {a, e, i, o, u} and {a, b, c, d} are 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.

Answer 1

i) Rule: If two sets are disjoint their intersection is null set. 

= {2, 3, 4, 5} n {3, 6} = { 3 } ≠ φ 

∴ Given statement is False.

ii) Given sets are 

{a, e, i, o, u} and {a, b, c, d} 

= {a, e, i, o, u} ∩ {a, b, c, d} 

= { a } ≠ φ 

∴ Given statement is False. 

iii) Given sets are 

{2, 6, 10, 14} and {3, 7, 11, 15} 

= {2, 6, 10, 14} ∩ {3, 7, 11, 15} 

= { } 

∴ Given statement is True. 

iv) Given sets are 

{2, 6, 10} and {3, 7, 11} 

= {2, 6, 10} ∩ {3, 7, 11} = { } 

∴ Given statement is True.