State whether each of the following ...

NCERT Class XI Mathematics - Sets - Solutions

Question : 42 of 73

Marks: +1, -0

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:

(i) Let A = {2, 3, 4, 5} and B = {3, 6}

Now A ∩ B = {2, 3, 4, 5} ∩ {3, 6} = {3}.

Since A ∩ B ≠ ϕ

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

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

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

Since A ∩ B ≠ ϕ

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

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

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

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 ∩ B = {2, 6, 10} ∩ {3, 7, 11} = ϕ

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

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