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

Step-by-step explanation:

1) False

A={2,3,4,5} B={3,6}

A∩B={3}

So, A and B are not disjoint sets.

2) False

A={a,e,i,o,u} , B={a,b,c,d}

A∩B={a}

Hence, A and B are not disjoint sets.

3) True

A={2,6,10,14} ,B={3,7,11,15}

A∩B=ϕ

Hence, A and B are disjoint sets.

4) True

A={2,6,10} ,B={3,7,11}

A∩B=ϕ

Hence, A and B are disjoint sets.

Answer 2

Step-by-step explanation:

(i) False

A={2,3,4,5} B={3,6}

⇒A∩B={3}

So, A and B are not disjoint sets.

(ii) False

A={a,e,i,o,u} , B={a,b,c,d}

A∩B={a}

Hence, A and B are not disjoint sets.

(iii) True

A={2,6,10,14} ,B={3,7,11,15}

A∩B=ϕ

Hence, A and B are disjoint sets.

(iv) True

A={2,6,10} ,B={3,7,11}

A∩B=ϕ

Hence, A and B are disjoint sets.