Solved Example of Equal Sets
Problem 1. Are the sets P = {r: r is prime such that 40 < r < 50} and Q = {42, 44, 45, 46, 48} equal?
Solution:
Set P = {r: r is prime such that 40 < r < 50} and set Q = {42, 44, 45, 46, 48, 49}.
Thus, P = set of prime numbers between 40 and 50.
⇒ P = {41, 43, 47} ≠ {42, 44, 45, 46, 48, 49} = Q
Thus, sets P and Q are unequal.
Problem 2. Identify the equal sets from the following:
P = {p ∈ R: p2– 2p + 1 = 0}
Q = (1, 2, 3}
R = {p ∈ R : p3 – 6p2 + 11p – 6 = 0}.
Solution:
Two sets are regarded as equal sets when they have all the same elements and also the same number of elements.
Let’s list out the elements of sets P and R before comparing them with set Q.
P ={p ∈ R: p2 – 2p + 1 = 0}
⇒ p2 – 2p + 1 = 0
⇒ (p – 1)2 = 0
∴ p = 1.
⇒ P = {1}
Set Q can also be written as {1, 2, 3} since we do not repeat elements in a set.
Similarly, upon solving p3 – 6p2 + 11p – 6 = 0, set R = {1, 2, 3}.
Thus, sets Q and R are equal.
Problem 3. Determine the groups of equivalent and equal sets from the following: A = {0, $}, B = {10, 21, 39, 94}, C = {44, 89, 128}, D = {39, 10, 21, 94}, E = {1, 0}, F = {89, 44, 128}, G = {15, 5, @, 11}, H = {a, c}.
Solution:
Equivalent Sets:
Having 2 elements each: A, E and H
Having 3 elements each: C and F
Having 4 elements each: B, D and G
Equal Sets:
B and D = {10, 21, 39, 94}
C and F = {44, 89, 128}
Problem 4. Determine whether the sets of alphabets in words TITLE and LITTLE are equal.
Solution:
Let A be the set of alphabets in the word TITLE.
A = {L, I, T, E}
Let B be the set of alphabets in the word LITTLE.
B = {L, I, T, E}
Thus, A and B are equal sets.
Equal Sets: Definition, Cardinality, and Venn Diagram
Equal Set is the relation between two sets that tells us about the equality of two sets i.e., all the elements of both sets are the same and both sets have the same number of elements as well. As we know, a set is a well-defined collection of objects where no two objects can be the same, and sets can be empty, singleton, finite, or infinite based on the number of its elements.
Other than that, there can be sets based on the relationships between two sets such as subsets, equivalent sets, equal sets, or it can set of subsets for any set, i.e., power sets, etc. This article explores one such relationship of sets known as Equal Set, including definition, examples, properties as well as Venn diagram.
Table of Content
- What are Equal Sets?
- Equal Sets Definition
- Equal Set Symbol
- Example of Equal Sets
- Equal and Equivalent Sets
- Venn Diagram of Equal Sets
- Properties of Equal Sets
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