If A = {3, 5, 7, 9, 11}, B = {7, 9, 11, 13}, C = {11, 13, 15} and D = {15, 17}; find
(i) \(A ∩B\)
(ii) \(B ∩C\)
(iii) \(A ∩C ∩D\)
(iv) \(A ∩C\)
(v) \(B ∩D\)
(vi) \(A ∩(B ∪ C)\)
(vii) \(A ∩D\)
(viii) \(A ∩(B ∪ D)\)
(ix) \((A ∩B) ∩(B ∪ C)\)
(x) \((A ∪ D) ∩(B ∪ C)\)
(i) \(A ∩B\)
(ii) \(B ∩C\)
(iii) \(A ∩C ∩D\)
(iv) \(A ∩C\)
(v) \(B ∩D\)
(vi) \(A ∩(B ∪ C)\)
(vii) \(A ∩D\)
(viii) \(A ∩(B ∪ D)\)
(ix) \((A ∩B) ∩(B ∪ C)\)
(x) \((A ∪ D) ∩(B ∪ C)\)
Solution and Explanation
(i) \(A ∩B \)= {7, 9, 11}
(ii) \(B ∩C\) = {11, 13}
(iii) \(A ∩C ∩D = \){ \(A ∩C\)} \(∩D\) = {11} \(\cap\){15, 17} = \(\phi\)
(iv) \(A ∩C =\) {11}
(v) \(B ∩D = \phi\)
(vi) \(A ∩(B ∪ C) = (A ∩B) (A ∩C)\)
= {7, 9, 11} {11} = {7, 9, 11}
(vii) \(A\cap D = \phi\)
(viii) \(A ∩(B ∪ D) = (A ∩B) (A ∩D)\)
= {7, 9, 11} Φ= {7, 9, 11}
(ix) \((A ∩B) ∩(B ∪ C) =\) {7, 9, 11}\(\cap\){7, 9, 11, 13, 15} = {7, 9, 11}
(x) \((A ∪ D) ∩(B ∪ C)\) = {3, 5, 7, 9, 11, 15, 17) \(\cap\){7, 9, 11, 13, 15}
= {7, 9, 11, 15}
Top Questions on Universal Set
- 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
- Mathematics
- Universal Set
- 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) \( (A')'\)
(vi) \((B-C)'\)- CBSE Class XI
- Mathematics
- Universal Set
- 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.- CBSE Class XI
- Mathematics
- Universal Set
- If R is the set of real numbers and Q is the set of rational numbers, then what is R - Q?
- CBSE Class XI
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- Universal Set
- If X = {a, b, c, d} and Y = {f, b, d, g}, find
(i) X - Y
(ii) Y - X
(iii) X \(\cap\) Y- CBSE Class XI
- Mathematics
- Universal Set
Questions Asked in CBSE Class XI exam
- Draw formulas for the first five members of each homologous series beginning with the following compounds.\((a) H–COOH (b) CH_3COCH_3 (c) H–CH=CH_2\)
- CBSE Class XI
- Organic Chemistry- Some Basic Principles and Techniques
- Distinguish between the following pairs of sentences.
(i) He was visibly moved.
(ii) He was visually impaired.- CBSE Class XI
- The adventure
- How, according to you, can peace and liberty be maintained in a state?
- CBSE Class XI
- The tale of melon City
Figures 9.20(a) and (b) refer to the steady flow of a (non-viscous) liquid. Which of the two figures is incorrect ? Why ?
- CBSE Class XI
- Pressure
- Describe the change in hybridisation (if any) of the Al atom in the following reaction.
\(AlCl_3+Cl^- \rightarrow AlCl_4^-\)- CBSE Class XI
- Hybridisation
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”