From the sets given below, select equal sets:
A = {2, 4, 8, 12}, B = {1, 2, 3, 4}, C = {4, 8, 12, 14}, D = {3, 1, 4, 2}
E = {-1, 1}, F = {0, a}, G = {1, -1}, H = {0, 1}
A = {2, 4, 8, 12}, B = {1, 2, 3, 4}, C = {4, 8, 12, 14}, D = {3, 1, 4, 2}
E = {-1, 1}, F = {0, a}, G = {1, -1}, H = {0, 1}
Solution and Explanation
A = {2, 4, 8, 12}; B = {1, 2, 3, 4}; C = {4, 8, 12, 14}
D = {3, 1, 4, 2}; E = {-1, 1}; F = {0, a}
G = {1, -1}; A = {0, 1}
It can be seen that
\(8 ∈ A, 8 ∉ B, 8 ∉ D, 8 ∉ E, 8 ∉ F, 8 ∉ G, 8 ∉ H\)
\(⇒ A ≠ B, A ≠ D, A ≠ E, A ≠ F, A ≠ G, A ≠ H\)
Also, \(2 ∈ A, 2 ∉ C\)
\(∴ A ≠ C\)
\(3 ∈ B, 3 ∉ C, 3 ∉ E, 3 ∉ F, 3 ∉ G, 3 ∉ H\)
\(∴ B ≠ C, B ≠ E, B ≠ F, B ≠ G, B ≠ H\)
\(12 ∈ C, 12 ∉ D, 12 ∉ E, 12 ∉ F, 12 ∉ G, 12 ∉ H\)
\(∴ C ≠ D, C ≠ E, C ≠ F, C ≠ G, C ≠ H 4\)\(∈ D, 4 ∉ E, 4 ∉ F, 4 ∉ G, 4 ∉ H\)
\(∴ D ≠ E, D ≠ F, D ≠ G, D ≠ H\)
Similarly, \(E ≠ F, E ≠ G, E ≠ H\)
\(F ≠ G, F ≠ H, G ≠ H\)
The order in which the elements of a set are listed is not significant.
∴ B = D and E = G
Hence, among the given sets, B = D and E = G.
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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.