State whether each of the following statement is true or false. Justif

1.	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» 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.

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»

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.