Question

State whether each of the following statements 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) Let A = {2, 3, 4, 5} and B = {3, 6}

Now $A\cap B$ = {2, 3, 4, 5} $\cap$ {3, 6} = {3}

Hence A and B are not disjoint. So the statement is false.

(ii) Let A = {a, e, i, o, u} and B = {a, b, c, d}

Now $A\cap B$ = {a, e, i, o, u} $\cap$ {a, b, c, d}

= {a}

Hence A and B are not disjoint. So the statement is false.

(iii) Let A = {2, 6, 10, 14} and B = {3, 7, 11, 15}

Now $A\cap B$ = {2, 6, 10, 14} $\cap$ {3, 7, 11, 15} = $\Phi$

Hence A and B are disjoint sets. So the statement is true.

(iv) Let A = {2, 6, 10} and B = {3, 7, 11}

Now $A\cap B$ = {2, 6, 10} $\cap$ {3, 7, 11} = $\Phi$

Hence A and B are disjoint sets. So the statement is true.