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.

Solution:

A pair of sets is said to be disjoint when there are no common elements in them.

i.e., two sets A and B are disjoint if A ∩ B = Φ.

(i) We have 3 ∈ {2, 3, 4, 5} and 3 ∈ {3, 6}

Therefore, {2, 3, 4, 5} ∩ {3, 6} = {3} and hence they are NOT disjoint.

Thus, the given statement is FALSE.

(ii) We have a ∈ {a, e, i, o, u} and a ∈ {a, b, c, d}

Therefore, {a, e, i, o, u} ∩ {a, b, c, d} = {a} and hence they are NOT disjoint.

Thus, the given statement is FALSE.

(iii) We have {2, 6, 10, 14} ∩ {3, 7, 11, 15} = Φ and hence they are disjoint.

Thus, the given statement is TRUE.

(iv) We have {2, 6, 10} ∩ {3, 7, 11} = Φ and hence they are disjoint.

Thus, the given statement is TRUE

NCERT Solutions Class 11 Maths Chapter 1 Exercise 1.4 Question 12

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.

Summary:

We are asked to state whether each of the following statements is true or false. We found that:
(i) "{ 2, 3, 4, 5 } and { 3, 6} are disjoint sets" is FALSE.
(ii) "{ a, e, i, o, u } and { a, b, c, d } are disjoint sets" is FALSE.
(iii) "{ 2, 6, 10, 14 } and { 3, 7, 11, 15} are disjoint sets" is TRUE.
(iv) "{ 2, 6, 10 } and { 3, 7, 11} are disjoint sets" is TRUE.