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.
Top Questions on Universal Set
- Let \( U \) be the universal set, and \( A \) and \( B \) be the subsets of \( U \). If \( n(U) = 450 \), \( n(A) = 200 \), \( n(B) = 205 \), and \( n(A \cap B) = 15 \), then \( n(\overline{A}\cap \overline{B}) \) is equal to:
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(ii) A - C
(iii) A - D
(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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- Let U ={1, 2, 3; 4, 5, 6, 7, 8, 9}, A = {1, 2, 3, 4}, B = {2, 4, 6, 8} and C = {3, 4, 5, 6}. Find
(i) \(A'\)
(ii) \(B'\)
(iii) \((A ∪ C)'\)
(iv) \((A ∪ B)'\)
(v) \( (A')'\)
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Answer the following :
(a) The casing of a rocket in flight burns up due to friction. At whose expense is the heat energy required for burning obtained? The rocket or the atmosphere?
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(c) An artificial satellite orbiting the earth in very thin atmosphere loses its energy gradually due to dissipation against atmospheric resistance, however small. Why then does its speed increase progressively as it comes closer and closer to the earth ?
(d) In Fig. 5.13(i) the man walks 2 m carrying a mass of 15 kg on his hands. In Fig. 5.13(ii), he walks the same distance pulling the rope behind him. The rope goes over a pulley, and a mass of 15 kg hangs at its other end. In which case is the work done greater ?
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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”