Which of the following are examples of the null set
(i) Set of odd natural numbers divisible by 2
(ii) Set of even prime numbers
(iii) {x: x is a natural numbers, x < 5 and x > 7 }
(iv) {y: y is a point common to any two parallel lines}
(i) Set of odd natural numbers divisible by 2
(ii) Set of even prime numbers
(iii) {x: x is a natural numbers, x < 5 and x > 7 }
(iv) {y: y is a point common to any two parallel lines}
Solution and Explanation
(i) A set of odd natural numbers divisible by 2 is a null set because no odd number is divisible by 2.
(ii) A set of even prime numbers is not a null set because 2 is an even prime number.
(iii) {x: x is a natural number, x < 5 and x > 7} is a null set because a number cannot be simultaneously less than 5 and greater than 7.
(iv) {y: y is a point common to any two parallel lines} is a null set because parallel lines do not intersect. Hence, they have no common point.
Top Questions on The Empty Set
Questions Asked in CBSE Class XI exam
- Identify the substance oxidised, reduced, oxidising agent and reducing agent for each of the following reactions:
- \(2AgBr (s) + C_6H_6O_2(aq) \rightarrow 2Ag(s) + 2HBr (aq) + C_6H_4O_2(aq)\)
- \(HCHO(l) + 2[Ag (NH_3)_2] ^+ (aq) + 3OH^ - (aq) \rightarrow 2Ag(s) + HCOO ^- (aq) + 4NH_3(aq) + 2H_2O(l)\)
- \(HCHO (l) + 2Cu^{ 2+}(aq) + 5 OH^ - (aq) \rightarrow Cu_2O(s) + HCOO ^- (aq) + 3H_2O(l)\)
- \(N_2H_4(l) + 2H_2O_2(l) \rightarrow N_2(g) + 4H_2O(l)\)
- \(Pb(s) + PbO_2(s) + 2H_2SO_4(aq) \rightarrow 2PbSO_4(s) + 2H_2O(l)\)
- CBSE Class XI
- Oxidation Number
Figure 8.9 shows the strain-stress curve for a given material. What are (a) Young’s modulus and (b) approximate yield strength for this material?
- CBSE Class XI
- Stress-strain curve
- Arrange the bonds in order of increasing ionic character in the molecules: LiF, K2O, N2, SO2 and ClF3.
- CBSE Class XI
- Molecular Orbital Theory
- Three reasons why the author’s grandmother was disturbed when he started going to the city school.
- CBSE Class XI
- The Portrait of a lady
Two identical ball bearings in contact with each other and resting on a frictionless table are hit head-on by another ball bearing of the same mass moving initially with a speed V. If the collision is elastic, which of the following (Fig. 5.14) is a possible result after collision ?
- CBSE Class XI
- Collisions
Concepts Used:
Types of Sets
Sets are of various types depending on their features. They are as follows:
- Empty Set - It is a set that has no element in it. It is also called a null or void set and is denoted by Φ or {}.
- Singleton Set - It is a set that contains only one element.
- Finite Set - A set that has a finite number of elements in it.
- Infinite Set - A set that has an infinite number of elements in it.
- Equal Set - Sets in which elements of one set are similar to elements of another set. The sequence of elements can be any but the same elements exist in both sets.
- Sub Set - Set X will be a subset of Y if all the elements of set X are the same as the element of set Y.
- Power Set - It is the collection of all subsets of a set X.
- Universal Set - A basic set that has all the elements of other sets and forms the base for all other sets.
- Disjoint Set - If there is no common element between two sets, i.e if there is no element of Set A present in Set B and vice versa, then they are called disjoint sets.
- Overlapping Set - It is the set of two sets that have at least one common element, called overlapping sets.