Which of the following pairs of sets are disjoint
(i) {1, 2, 3, 4} and {x: x is a natural number and \(4 ≤ x ≤ 6\)}
(ii) {a, e, i, o, u} and {c, d, e, f}
(iii) {x: x is an even integer} and {x: x is an odd integer}
(i) {1, 2, 3, 4} and {x: x is a natural number and \(4 ≤ x ≤ 6\)}
(ii) {a, e, i, o, u} and {c, d, e, f}
(iii) {x: x is an even integer} and {x: x is an odd integer}
Solution and Explanation
(i) {1, 2, 3, 4}
{x: x is a natural number and \(4≤ x ≤ 6\)} = {4, 5, 6}
Now, {1, 2, 3, 4} \(\cap\) {4, 5, 6} = {4}
Therefore, this pair of sets is not disjoint.
(ii) {a, e, i, o, u} \(\cap\) (c, d, e, f} = {e}
Therefore, {a, e, i, o, u} and (c, d, e, f} are not disjoint.
(iii) {x: x is an even integer} \(\cap\) {x: x is an odd integer} =\(\phi\)
Therefore, this pair of sets is disjoint.
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(ii) A - C
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(iv) B - A
(v) C - A
(vi) D - A
(vii) B - C
(viii) B - D
(ix) C - B
(x) D - B
(xi) C - D
(xii) D - C- CBSE Class XI
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- Taking the set of natural numbers as the universal set, write down the complements of the following sets:
(i) {x: x is an even natural number}
(ii) {x: x is an odd natural number}
(iii) {x: x is a positive multiple of 3}
(iv) {x: x is a prime number}
(v) {x: x is a natural number divisible by 3 and 5}
(vi) {x: x is a perfect square}
(vii) {x: x is perfect cube}
(viii) {x: x + 5 = 8}
(ix) {x: 2x + 5 = 9}
(x) {x: \(x ≥ 7\)}
(xi) {x: x \(\in\) N and \(2x + 1 > 10\)}- CBSE Class XI
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(ii) \(B'\)
(iii) \((A ∪ C)'\)
(iv) \((A ∪ B)'\)
(v) \( (A')'\)
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(iii) {2, 6, 10, 14} and {3, 7, 11, 15} are disjoint sets.
(iv) {2, 6, 10} and {3, 7, 11} are disjoint sets.- CBSE Class XI
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Give reasons for the following.
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Concepts Used:
Operations on Sets
Some important operations on sets include union, intersection, difference, and the complement of a set, a brief explanation of operations on sets is as follows:
1. Union of Sets:
- The union of sets lists the elements in set A and set B or the elements in both set A and set B.
- For example, {3,4} ∪ {1, 4} = {1, 3, 4}
- It is denoted as “A U B”
2. Intersection of Sets:
- Intersection of sets lists the common elements in set A and B.
- For example, {3,4} ∪ {1, 4} = {4}
- It is denoted as “A ∩ B”
3.Set Difference:
- Set difference is the list of elements in set A which is not present in set B
- For example, {3,4} - {1, 4} = {3}
- It is denoted as “A - B”
4.Set Complement:
- The set complement is the list of all elements present in the Universal set except the elements present in set A
- It is denoted as “U-A”