NCERT Class XI Mathematics - Sets - Solutions
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Question : 42
Total: 73
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.
(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.
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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