Question

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) {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) False
As 3 \(\in\) {2, 3, 4, 5}, 3 \(\in\) {3, 6}
\(⇒\) {2, 3, 4, 5} \(\cap\) {3, 6} = {3}

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(ii) False
As a \(\in\) {a, e, i, o, u}, a \(\in\) {a, b, c, d}
\(⇒\) {a, e, i, o, u } \(\cap\) {a, b, c, d} = {a}

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(iii) True
As {2, 6, 10, 14} \(\cap\) {3, 7, 11, 15} = \(\phi\)

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(iv) True
As {2, 6, 10} \(\cap\) {3, 7, 11} = \(\phi\)